It depends on where you got the fish from. The turtles will always have *some* parasites. It is just natural ... it only becomes a problem when the parasites *bloom* because of some sort of natural force acting on the turtle forcing the parasite population out of whack. It is entirely possible that the fish were the source of the bloom in the first place. If you purchased them from a pet store around the same time that the turtle's behavior changed then I would certainly suspect them as the initial cause. It is common for certain pet stores to carry *bad* fish for turtles. Your solution would be to merely find another pet store to purchase fish that cohabitate with turtles from.
But to answer your initial question - - yes, it is possible and I would relocated them to a different tank it it were me.