Yep. Sure, Bettas can live in 1 gallon bowls. So long as you keep their water crystal clear, at a stable, warm temperature, they will do fine.
Keeping Bettas in a 1 gallon bowl is like keeping a human in a white room, with nothing in it. Sure, it gets cleaned every day, they're fed properly, but wouldn't you get a little... bored?
If you were kept in a large room, with lots of things to do and see, you'd be fine, right?
If a Betta was kept in a large tank with different hiding places, caves, spots with certain different flow to others, and generally more stuff to do, it would feel more secure and happy, right?
It's the same principle.