It is true that Bettas don't permanantly live in puddles and this would be very uncomfortable and miserable for them but there are times when rice paddy fields dry up, I belive I read somewhere that rice has to go through a "dry stage" which is when the rice it is mostly sown into the ground, so that would leave water very scarce and so the betta fish would be forced to live for a short
period of time in very little water.
Living in "puddles" and very small amounts of water is a last resort for the animal though and isn't very pleasant for it and as keepers of animals we should do all in our power to make them as comfortable and well looked after as we can. I think a 1 gallon tank is the very least I'd provide a betta with although I'd probably opt for a 2 or 3 gallon.
(if I'm wrong about anything then please feel free to correct me)
A small amount of water in a paddy field, if you look closely you might spot a fish, not sure what type it is.