Apple is hosting user created content though (in the form of apps). Don't they become liable for that hosting if they don't handle the DMCA request themselves?
In effect, you'd be triggering the same sequence that led to youtube-dl being blocked on GitHub for a while. Surely, GitHub = Microsoft didn't build it, but they still had to block access when the RIAA sent a DMCA.
In the youtube-dl case, the DMCA notice was later found to be fraudulent and thus the access was restored. But if the infringing app re-uses images verbatim, that won't happen so it stays offline.