Actually, looking at Wishiwashi’s schooling form, maybe it’s allowed because the school seems to fuse together? With the “main” Wishiwashi serving as the “brain” of the school itself? I mean, it could just be graphical limitations, but the school does look like it fuses into a single organism.

Well, “seems” is the operative word there – the whole point of Wishiwashi’s design is that it’s based on schools of fish that are able to make it look like they’re a single organism even though they definitely aren’t.  This rationale might save us from having to explain why Wishiwashi is basically allowed to cheat in Pokémon battles, but I think it does so at the expense of what makes Wishiwashi an interesting Pokémon.