Private messages are not indexed by google or other search engines.

In other forums I have been involved in, it is typical for a certain limited number of staff- most often admin only, or sometimes one or two selected higher admin- to have the permissions to read private messages.

However, the frequency with which they do so, in my experience, tends to be very limited. Or should be, in my opinion.

In my experience, the actual occurrence in which PMs are read has been very rare, and only in the interest of safety- when there is great concern for the members involved or where there may be a situation that can only be resolved by reading a message to figure out facts or details of a situation that is unclear.

In my opinion, I would say it is important to have this as a limited permission but to have it only be exercised in a very limited capacity.

Obviously it would be up to the staff of PC to answer for THIS forum, but it is not uncommon for some number of the staff to have permissions to read messages between members. Same goes for chat logs.
The frequency that this is done would depend on the forum and the individual policies of each forum.