If water conditions are kept up, I find nothing wrong with 1 gallon tanks. In fact, my first rescue was in a 1 gallon tank and he healed up quite well.
I wasn't sure if he was gonna live so i just got the $10 hawkeye 1 gallon tank. I dislike it because it is hard to get the betta out of it when its time for a water change.
His fins started growing back and he colored up which I doubt he would of done if he was not kept in clean water. I did not, however have a heater for him at the time and I ended up ditching the undergravel filter.
He he is a few weeks later - the water is green because of Betta Revive.
Although, I will admit, he started healing A LOT faster when I put him into the 5 gallon.