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There's a belief held by some that if a picture is on the Internet it's fair game for use in any way. I know someone who found some of his pictures published in a book. The author claimed they were not stolen but the author's own pictures. The problem was that the real owner of the pictures was in some of those pictures. Also there is a fair use policy covering academic applications although that is frequently abused by using the pictures online rather than in a teaching environment.

The developer of the website probably figured there's 20 million cats in the USA and what's the possibility of one cat's picture being found by the animal's owner. Evidently 100%

The rescue group should have asked permission even after the fact rather than being hostile. That shows no class at all!