On February 8, 2011, this question was addressed in this thread, A Question about Private Messages…, http://forums.hannity.com/showthread.php?t=2187981 .
The OP noted a thread which had been posted by Rick but which then disappeared. The contents of the original thread are at odds with what Rick posted later.
Rick on 2/7/2011, from a cached version of the thread which disappeared, about the user Msny:
Banned for recruiting posters away from this board via pm.
LadyGunSlinger’s ban is permanent as well. Going through the account’s PM’s, there may be several more to follow.
Rick on 2/8/2011:
No. Put the tinfoil hat away.
We cannot see private messages. The messages I was referring to are messages forwarded to us by others.
Furthermore, Rick sent a warning PM to another member in connection with this incident saying that once an account is banned the password can be changed and the PMs can be accessed.
Update: Here is a screenshot of the deleted TTTM thread. Click for full size: 945px × 2,245px.
Having the ability to access those PMs could be reasonable for moderators in case there was probable cause for suspecting literal abuse or for other matters literally affecting board security. However, it is not good for moderators to be able to do this when they are known for banning arbitrarily and regularly turning the bans into simple timeouts if the members are willing to apologize for offenses real or imagined and request reinstatement. The banned member might not wish to request reinstatement on a board with abusive moderators. However, they might, and by the time their ban is commuted to a timeout their account could already have been hacked.
Finally for now, there is also still an open question about whether the moderators at Hannity would take advantage of techniques which are readily available at V-Bulletin hack sites for reading the PMs of currently active members. The Hannity moderators do not inspire confidence in this matter.