It is probably both. They train in normal water, so they know what it feels like, but when it comes to getting hit and tackled, and shooting, there's no way someone would still be able to keep their breath in -- it's not possible. The pyrefly saturated water might be able to aid the players in some way to keep their mouths closed, yet still maintain the strength to perform any action underwater.
It could also potentially explain why Evrae was turned into a Zombie so quickly, and could survive under the Purifico (FFX, Excape from Bevelle). I've always wondered about that one that too. Doesn't seem that a Zombie would form so quickly.