Clearly, on some level, it is possible, because you do have these trained bears that appear in movies. But when you start talking about wild bears, the answer is no.
I was a tour guide in Yellowstone National Park for a few years, and while I was there, there were a handful of people who were killed by bears. The reasons varied, but eventually what it boils down to is people not respecting the animal, and thinking that, because they’re inside of a park, it might be slightly safer.
You do have examples of places like the Brooks Range in Alaska, where the bears are well-fed and there’s a cascading waterfall, which makes it a really good spot for bears to catch salmon. You’ll get more than a dozen bears gathered right there, and you’ll have people there as well, and they’ve never had a human killed by a bear at that spot, partially because there is so much food that they don’t feel competition.
But in Yellowstone National Park, where bears are much less likely to see humans early on in their lives, and where they’re not as accustomed to humans, absolutely not. For the most part, every single bear that I’ve seen in the wild has either ignored me completely, or run away at the sight of me.
There’s an ongoing theory that we have inadvertently bred out the aggressive gene in grizzly bears. If you go back and read Lewis and Clark’s journals, you will see these passages where they shoot a bear, and then the bear chases them for like a half mile while they’re shooting it, and by the time the bear finally dies it has eight bullets in it.
The theory is that the aggressive bears were the ones that were killed, and the shyer bears retreated into the mountains, and those are the bears we have left today. But even so, they’re still not our friends.
From a policy standpoint, you don’t want bears associating people with food. That’s a big problem. Once they start associating people with food, they’re going to start hanging around people, and it’s just a matter of time before something bad happens.
See the full post with other answers from Doug Peacock, Shannon Donahue, Thomas McNamee, Fred Koontz, Gordon M. Burhardt, and Dr. Oded Berger-Tal.