Contrary to popular belief, betta do not come from mud puddles. They come from Thailand (used to be called Siam, hence "Siamese Fighting Fish") and live in rice paddies, these usually are a good 12 inches deep and can be acres wide.
The rice paddies are huge, and yes, shallow. They're very weed-choked and slow moving bodies of water. The thick vegetation provides plenty of hiding places which is important for betta.