OK, yes, just one counterexample would disprove it. But that means nothing unless you can find one counterexample. Can you?
Depends. To what standard of proof? Genealogical records? Generally, I think firing off a question to MyHeritage or 23andMe might do it.
Statistically, I believe it is overwhelmingly probable that an outlier exists somewhere. Some mountain village or similar where the same twelve families have been marrying each other for fifteen hundred years.
Genetically, we have populations that show no ingression from other populations for far longer than what is necessary, but we cannot preclude that such genes have been lost. Although it seems unlikely based on other cases.
Show your work. Because the people who have actually done the statistics have concluded that it’s overwhelmingly improbable. Saying that you have a hunch what the math would say doesn’t hold a candle to actually doing the math.
OK, what village is that, where? Sure, you can find villages where it’s mostly the same twelve families intermarrying, but do you really think that there hasn’t been one traveling trader who seduced a farmer’s daughter while passing through, or one criminal laying low and hiding from the law who raped one, or one villager who wanted to see what was over the next hill and brought back a spouse? None at all, for thousands of years? What species populates this village, because humans sure don’t act like that.
23andme wouldn’t confirm or deny this. As I mentioned in my last post, after 10 generations there’s a 50/50 chance you will inherit no DNA from an ancestor. In theory it’s even possible to inherit no DNA from a grandparent. (Although this is almost impossible.) You could theoretically be genealogically 25% black or Native American, but have 100% European genes.
The OP asked the question are “we” at most 50th cousins, but did not specify what “we” means. If “we” means every single human alive on the planet (all 8 billion of them), that’s a different answer than if “we” meant IceQube and his girlfriend. I think we can safely rule out the possibility that IceQube’s girlfriend comes from a previous uncontacted tribe that has been isolated for thousands of years. I submit to you that if you go on a date and you say to your date, “You and I are, at most, 50th cousins.” there is at least a 99% chance that you are telling the truth. The mere fact that you and your date are speaking a common language suggests that your ancestors mixed with your date’s ancestors within the last few centuries.
Another interpretation of “we” could be all the people who might participate in the straight dope message board, which again pretty much falls to people who speak English with some degree of fluency. In fact, I’d be willing to wager that the probability of two speakers of English being related within N generations is greater than 99% for some values of N smaller than 50. It wouldn’t surprise me at all if you could get N down to 20 or 30.
A scientific paper published in 2013 found that “most people alive today in Europe share nearly the same set of (European, and possibly world-wide) ancestors from only 1,000 years ago”, which they estimated to be 33 generations. That’s all over Europe, with people who speak different languages from each other. They also found “pairs of individuals across Europe are reasonably likely to share common genetic ancestors within the last 1,000 years, and are certain to share many within the last 2,500 years. From our numerical results, the average number of genetic common ancestors from the last 1,000 years shared by individuals living at least 2,000 km apart is about 1/32 (and at least 1/80); between 1,000 and 2,000ya they share about one; and between 2,000 and 3,000 ya they share above 10.” Notice the part about living more than 2,000 km apart. It’s very unlikely that IceQube and his girlfriend speak different languages and live more than 2,000 km apart. But if they do, they’d still share a common ancestor within 2,000 years = 66 generations.
If you are going to parse the OP, note that he doesn’t ask about “we”, but about “we all”. I think the “all” is strongly indicative of him asking about everyone alive today.
Challenge accepted.
The wiki article linked upthread about the Most Recent Common Ancestor (MRCA) says that mitocondrial Eve lived approximately 200,000 years ago, and Y-chromosomal Adam was between 237,000 and 581,000. Doesn’t that mean that our MRCA lived around 200,000 years ago, making it every difficult for us all to be 50th cousins?
No, Y-Adam and mt-Eve are both common ancestors, but neither is the most recent common ancestor. Y-Adam is the man who was everyone’s father’s father’s father’s father’s father’s … father’s father. Mt-Eve is the woman who was everyone’s mother’s mother’s mother’s mother’s … mother’s mother. But there might be someone else who’s my mother’s father’s father’s father’s mother’s … mother’s mother, and your father’s mother’s mother’s father’s … father’s mother, or any other combination of parents.
Australia Aborigines are one group I really wonder about in this theory. They’ve only really been in contact with the outside world since 1788. For some of the oldest Aborigines this would only be about 5 generations before their birth.
I’m not aware of any real evidence of people traveling from Indonesia to Australia before Europeans landed on the island. It’s possible this happened but it’s pretty much unproven.
And even if an Indonesian got shipwrecked in Australia 1,000 years ago it’s not a given that this person would be an ancestor of all Aborigines alive today. Or even be an ancestor of any Aborigines. I think the Indonesian might have gotten massacred on the spot, and at the very least would have had trouble finding a mate because of how odd he’d look to the Aborigines. And to take it a step further, it’s not a given that this Indonesian would have been descended from the current MRCA, since the MRCA would have been earlier 1,000 years ago.
One group of Aborigines that was particuarly isolated was the Tasmanians. Who seem to have been completely isolated from other Aborigines until the mid 1800s. Which for some of the oldest Tasmanians is only 2 or 3 generations before birth.
Even granting that full blooded Aborigines are rare it’s pretty presumptuous to say there are exactly zero full blooded Aborigines. Especially if you consider that Australia never had the same hypodescent principles that the United States had where the half breeds would get thrown into the minority population. (Which is why blacks and to a lesser extent Amerinds in the US have European ancestry.) In fact, they actually had a program up kidnap half blooded Aborigines in Australia in order to breed out their blood.
I’m not aware of any real evidence that people didn’t travel from Indonesia to Australia before Europeans landed in Aus and Indonesia. It’s possible that it didn’t happen, but it’s pretty unlikely, based on the fact that it was already happening at the earliest known contact, and also given the history of infectious disease in Aus.
I’m only quoting an extract from your post because I think the rest represents reasonable opinions even where I disagree with them. But this, the myth of the savage natives, is not supported by the well documented experience of escaped convicts, ship-wrecked sailors, or Indonesian traders.
I think that the concept of a “full blooded” person is abstract, quaint, and ahistoric.
There was a report recently seeming to confirm than humans sailed to Crete 130,000 years ago, possibly even Neandert(h)als.
Boats were in common use in Japan 20,000 years ago.
Once the early settlers got thru the ice barriers in N. America it’s estimated they reached the southern tip of S. America in well under a 1000 years. Most likely along the coast and aided by boats.
People got around quite quickly for a long time. Australia is so close to New Guinea (which is so close to …) that regular travel for trade or fishing had to occur. One doesn’t need to speculate about the rare, one off, blown off course boat. The numbers were far greater.
Just to be clear, they may have “traveled by boat”, but we wouldn’t expect the boats to have had sails.
We certainly do have archaeological evidence of Indonesian contact with Norther Australia, going back thousands of years. So Australia hasn’t been isolated from Asia since the Pleistocene.
The claim that we’re all 50th cousins is almost the same as a claim than any pair of us have a common ancestor from 500 AD. That’s certainly true for 99.99% of human pairs, but is it true for 100%?
It should be fun to try to guess who the 500 AD common ancestor would be. Kalahari Bushmen, Andamanese, Australians? Surely there was a 500 AD chieftain in Indonesia who had 1000 AD descendants that visited Mozambique (via Madagascar), Sentinel Island and Australia. That should be long enough ago to infiltrate into the pedigree of every Bushman or aboriginal Australian. Maybe.
But what about Eskimos? Are they descended from that Indonesian chieftain? Maybe not, but they don’t need to be. Perhaps an early Khan of the Göktürks living in 500 AD links the Eskimos to Australia, and Attila the Hun himself is the link connecting Bushmen and Eskimos. 
Or not. 99.9% of us are 50th cousins, but to make that 100% we’d want to look at specific plausible infiltration hypotheses.
Isn’t the onus on the person to prove contact? I mean, there’s no proof against the idea that the Romans sailed to the Americas in 53 BC. But there’s no proof for the idea either. Therefore the idea is not taken seriously by historianss.
Just came across a Wikipedia article on Makassan (an Indonesian group) contact with Australia.
Definitely going on by the 1700s, probably by the 1600s and just maybe by the 1500s.
These were traders who had an affect on the Aboriginal group that contacted. (Leaving even some Islamic influences behind.)
Given that people from that area (Borneo) traveled back and forth and settled in Madagascar on the other side of the Indian Ocean 2000 years ago, short, regular trips to Australia for trade would have been nothing.
The Makassan contact proves that the Aborigines could be friendly rather than hostile. So gene swapping ensues.
Australia wasn’t that isolated.