Any chance this animal is really wild?
That’s a tame cat. In my experience, bobcats are among the North American mammals most averse to humans being sort-of near, let alone within touching distance. I’d sooner believe that people were petting a wild bear.
Definitely. The only way you’d get that close to a wild one is if it was eating you.
Define “wild”.
If I was to WAG (which I will), I’d speculate that it, if not a wandering pet, it was a rescue as a kitten, raised by humans and then released into the wild. A mama bobcat is extremely unlikely to teach her kittens to approach humans and flop over for belly-rubbin’s, but a rescue cat won’t act like a raised-in-the-wild cat.
I got to pet a rescued mountain lion once; it purred. (Sounded like an idling Harley).
People “rescue” and raise bobcats as pets? Is that legal?
The first thing to assume about a wild animal exhibiting abnormal behavior like that, is that it’s sick. Very foolish behavior on the part of those people.
Beautiful cat, but yeah, if I saw what I thought was a wild animal acting that friendly I’d stay away. And if I knew somebody who had a tamed bobcat (assuming legality, or I doubt I’d be too friendly with them) I’d still be very careful about getting close. Those claws and teeth are quite a bit larger than the ones on your average domestic cat.
As a pet? Depends on where you live. Bobcats are considered exotic animals, and may require a special license to own. Or they may not. State Laws: Private Possession of Exotic Animals | Born Free USA
But there are plenty of wildlife rescue groups who will accept bobcats (kittens or grown) who have been injured or abandoned or their mother’s been killed, nurse them back to health (or adulthood) and release them back into the wild if they’re deemed fit. Here’s an article about one.
Are you sure its not a lynx?
It does look a little tall to be a bobcat.
I thought a bobcat *was *a lynx. 
ETA: Yes, bobcat, aka lynx rufus. There are several subspecies, some taller than others.
I’ve been within 6 feet of a wild bobcat. It was caught in a leg trap (not mine!). It was not happy and I would not have wanted to pet it.
If the caption on those pictures is true, then those people are some of the stupidest on the planet. Petting a wild bobcat would be slightly less safe than sticking your hand in a running garbage disposal.
Oh hell no. I have never, NEVER seen a bobcat. I have lived my whole life in bobcat territory, have been to many zoos and sanctuaries that technically had a sign that I was looking at terrain that included a bobcat. Never, ever seen one.
All bobcats are Lynx, not all lynx are bobcats.
Only bobcat I ever saw was in the Mojave desert crossing a road at night. They are legendarily wary and rarely sighted, even where common.
The black tipped tale suggests it’s a lynx, from the wiki photos an Iberian lynx. They are very endangered, and it could be part of a breeding program or something.
From the photo, I would describe that as a lynx. In any case, hand-raised bobcats can be quite friendly with humans. I’ve petted a couple. One stole my hat once and wouldn’t give it back.
It’s not unlikely that I have, too. I’d never have known it, though: They’re extremely stealthy, and the typical human won’t know they’re there unless the cat wishes it to be known.
And the people in those pictures are unquestionably foolish. I wouldn’t even initiate contact with a strange housecat (if it jumps on my lap or rubs up against my leg or the like, I’ll pet it, but not otherwise). As Calvin once observed, cats are pointy on five of their six ends, and their preferred way of communicating displeasure uses those pointy ends.
Crazy or not, those pictures are freaking adorable.