Fair use defences aren't automatic, and all go on a case-by-case basis. One of the major criteria is 'effect on the work's value'. Given how easy it is to find people (in this very thread, even) gleefully predicting the death of stock photo sites, it'd pretty easy for a lawyer to tear said defence apart.

Weird Al gets permission for all of his music. Even if the parody defence were valid, song licensing is pretty cheap, and defending lawsuits against artists signed with major labels is expensive.