No, this is false, Inklings and Octolings die in water because they can not swim, because they have no bones. So theoretically Inklings and octolings can still take showers.
There skin is thin and they don't have bones so only part of them can go into water at a time. This is proved in the actual game. They can take showers. If they got spayed with a power hose they would die though.
