To clarify, yes, only myself (as owner of the site) can read PMs. I do this only when there is a specific concern or issue that suggests a member may be misusing our PM system (e.g., spamming other users for a product or service). In the 22+ years we've been online, I have done it only a handful of times.
It is an extremely rare occasion where PMs are read (remember, we have over 500,000 members, so I don't have time to read PMs for any other reason). No other members of the community support team have access to this functionality (hence the reason they ask for a PM to be forwarded to be reviewed).
Every service you log in to today (Facebook, twitter, other forums, etc.) has this capability. PMs (or DMs or whatever) are never 100% private, as there are legitimate reasons (e.g., court order, law enforcement, etc.) where those messages may need to be accessed. We have never received a court order or other legal request for such access, FYI.