Maybe I could sign in with someone else's AppleId, then submit the resume. It has my email and phone number on it, so hopefully they would send correspondence to that email address and not the one associated w/ the AppleId.

Maybe this is a test. Maybe everyone who tries to login to jobs.apple.com is told "oh yeah... that AppleId is invalid," and then they wait and see what people do. If they give up, then they're not Apple material. If they cheat and use someone else's AppleId, then they're morals are found lacking. If they post about their experience on a public forum, then they're a security risk.