I think it's a myth.
From what I've heard, you can't go too deep due to water pressure. Diving into the water head first or hitting your head in the water could cause problems.
As for football, I think the issue is roughness with head impact causing damage to the implant. I guess it's just playing football with a good helmet and not wearing implants.
I have friends who have CIs and they swim. A couple are water polo players. Heard no complaints from them.
I also have friends who play football, but this was flag football. I don't know about tackle football. Never knew anyone who had CI and played tackle football.