Because, depending on your configured concurrency model, it may need to be able to spawn new processes/threads as other users, and this is not possible unless you have at least one process running with some privileges beyond that of the normal users. This usually means root. Even if not root, it needs to be a user/group privileged enough to be able to impersonate the other users, or it can't do its job.
The code running with greater privilege is kept to a minimum but at least some needs to be there, and this exploit potentially gives a route through to manipulate it.
FastCGI and similar can help here - it can push the creation of user specific processes away from Apache, making it harder to cross the barrier.