Do you have a cite for that?
Emphasis mine.
Some sources claim the lineage as coming from steak tartare, and somebody deciding to put heat to it.
About.com claims the following:
Here’s a cool NPR piece on the history of hamburger.
Here’s an excerpt from Ozersky’s book on the history of hamburgers (Warning:PDF file):
Emphasis mine. This all suggests, to me, that the hamburger is not descended from the meatball.
Says who? You could just as well say a hamburger is a sausage patty.
To your derision, I only say form follows function. Sphere to Disk.
You mean to tell me that there wasn’t a cook in some 17th century kitchen who flattened a meatball to taste it cooked? He was speeding the cooking process, to see if the Edel would like it. They might even have taken the leftover meatball batter4 and fried it and ate it between bread. What is your position on The Duke of Sandwich, Pulykamel? Do you really think he was the first to put meat between bread?
No on the Duke of Sandwich. I’m sure someone somewhere must have flattened a meatball. But I bet you dollars to donuts that somebody first fried up a steak tartare before deciding to add binders and stretchers etc to the patty. What’s the point of your argument? I contend a flattened meatball is NOT a hamburger. It’s a flattened meatball.
The idea that the lineage must have gone beef+binders+stretchers to pure beef is not correct. The original Hamburg steaks were usually made from cheap beef without stretchers. They started out as chopped or ground steak, not meatballs. Show me evidence otherwise.
Duke…Earl of sandwich. Whateever. Duchy la sangwich.
Eh, I missed that one, too.
The name “Hamburger (Frikadelle)” is the first clue.
Even tartare is never served alone. It’s traditional components are egg, bread, and various accoutrements, including, but not limited to, onions, capers, parsley, etc.
Generally, I prefer ground chuck, lightly rounded and flattened. I sprinkle on poultry seasoning, Lawry’s seasoned salt, and Worchestershire onto the patties after they’re formed. I don’t like hamburger less than medium well…I just don’t like the texture of rarer ground meat. We keep American cheese slices in the fridge for hamburgers and grilled cheese sandwiches, and I like to put the cheese on the patty while it’s cooking, so it melts. I toast the buns, and then we add the various condiments and veggies. I like potato salad and/or cole slaw for sides, but we rarely have them. We more usually have French fries, from fresh potatoes. I generally slice up an onion and cook it with the taters, and that, my friends, is an excellent side dish.
I think that ground sirloin has an excellent flavor but is much too lean for burgers. I don’t eat meat that comes in chubs any more…fortunately, we can afford better now, so I have banned that option from my kitchen.
Read the history above. The provenance of the dish is not from anything resembling a meatball by my definition. One source says they were literally pounded steaks. The original real American hamburgers do, however, seem to include chopped onions in the patty.
Tartare does not have bread in it. At least not any tartare I’ve had.
Then you agree that a hamburger isn’t just just beef. Otherwise, I might think you an American imperialist. 
That’s not what I said. And it is rather disingenous to suggest otherwise. Bread is a component. Tartare is traditionally served upon and with bread.
… or as one might say in a kitchen. Yesterday’s tartare is today’s Hamburger Frikadelle. It’s not like like America has never dumbed down a great food tradition. That would be shocking, huh?
It’s all forcemeat. Further categorization is nitpicking.
New here, are you? 
Made burgers Saturday night with nothing but 80/20 chuck, a light dusting of onion powder, and a couple of splashes of Worcestershire sauce. Didn’t make them quite as thin as I should’ve (they turned out a little on the rare side of medium for my taste) but overall verdict: nomlicious.
I know this is almost cliched on these boards, but…
Yes, Australians like their burgers with beetroot (“beets” to you 'Merkins).
I’m not asking you to like this style of burger. What I do request though, is that you buy some tinned beets, and just try some next time you make burgers at home.
It’s actually pretty good.
Last time I was in Australia I had this. It was pretty good. If I remember correctly that burger also had a fried egg on it.
I think it developed predominantly into a beef-only patty, but did include onions in its early inceptions. It is not, however, a “meatball,” which is the main point I’ve been arguing against.
It was honestly unclear as what you meant, because my main objection is to bread or other extenders being in the meat. Tartare is served upon bread. So is a hamburger. Frikadelle is generally not served on bread. I don’t understand your point in bringing it up, then. It just confirms my point. 
One of the finest burgers I ever had included smashed-up Ritz crackers in the ground beef, not just as an extender, but because the cracker bits acted like little sponges, holding on to extra fat and making the burger even juicier and tastier. So, there is some usefulness to the addition of breadlike material, beyond making the meat go farther. Personally, though, I’m all for simplicity.
I don’t view the hamburger as a “dumbing down” of any great food tradition (is “frikadelle” great now? It’s fine, but it ain’t the glory of a good, American hamburger). It’s the creation of a new food tradition, and one I would call great.
The traditional Hamburgerer Frikadelle literally means “Meatballs of Hamburg”. A frikadelle is a meatball- in the case of the Hamburger, a flattened meatball… but a meatball nonetheless. The Hamburger Frikadelle or Hamburger, the obvious namesake and progenitor of the American Hamburger was never just plain meat, it included additional flavorings, seasonongs, and binders. It’s an American misconception and some might say, perversion to serve a plain meatpatty and call it a hamburger. That, after all, is not a Hamburger, but chopped beef.
No, a Hamburger Frikadelle is not generally served on bread, that’s an American addition. But all of the components and ingredients of a traditional Tartare, if combined with the meat and cooked, makes a frikadelle. Coincidence…I think not. It’s a misconception that a Hamburger is just plain meat… America popularized the all-beef patty mostly because of corporate convenience and standardization. Its origins are much more flavorful and substantial.