Bettas can live in a gallon of water, sure. The only problem is that's like you living in a walk-in closet.
Bettas do really well in a five gallon tank. They also need a heater and thrive with a filter, and they do appreciate a light on a regular cycle. My crowntail shares a standard ten gallon with two zebra nerite snails, and they all get to live with lots of space, plants, and hideys. He's a happy boy; he even jumps out of the water for food.