Only theymos and Cyrus have access to IP logs, not the moderators. I would also be very surprised if it turned out they were arbitrarily looking up user's IP logs just for the fun of it without some prior suspicion or indication.
The
Cryptios people have IP-access too.
Indeed. I wanted also to reply to o_e_l_e_o about this aspect, but then I noticed that LoyceV was faster than me. However, I will mention theymos' statement about Cryptios, as maybe others don't know this yet:
Cryptios's main purpose is recovering accounts, but they can also do minor patroller-type things. They are neither admins nor global moderators. They have access to IP/security logs (not PMs), but each of their accesses to private info are logged and per-day-limited; even if their access was compromised, the damage would be limited.