Maybe I'm reading too much into your post, but they couldn't naturally breathe underwater. They weren't fish people. Blitzball players trained themselves for that - I believe in the extra ending video for FFX in the International version, there's a scene where Yuna is practicing holding her breath to get better at it herself. I'm pretty sure that when Sin attacked that town on the coast early on that many villagers drowned. There's no reason why the great heroes of Eorzea can't be assumed to have taken the same training, or maybe add in silly intro quests for that.
I also don't think there's any reason mages why can't cast shape air magic to perform water breathing spells specifically for Blitzball, or at least the Moogles.