I was thinking that the signature needed to be kept on the server, away from the attacker, because they could simply re-sign the message, but now I realize that

I was thinking that the signature needed to be kept on the server, away from the attacker, because they could simply re-sign the message, but now I realize that checking the signature first would prevent the routine from ever getting to the decrypt algorithm, and thus no information would be leaked, so the attack would fail.