There's also a chance that some priests within the system were valid - I'm sure some of the legitimate priesthood would have been motivated to get into the system if at all possible. I have heard it suggested (and I have no idea whether there is any actual evidence behind this at all or just some guy's theory) that Zacharias was the legitimate Aaronic High Priest, but his position was usurped. That would make John the Baptist the legitimate High Priest after him. That in turn would explain why so many people were willing to go out to the desert to listen to John - they knew he had legitimacy. And it most importantly explains why John had to baptise Jesus - this was a passing-on-the-mantle moment. Now all that might be bollocks. But Jesus' circumcision etc may have been performed by a legitimate priest.