I don’t think moderators should be able to access members’ messages, except for official warning messages. We use the User Note plugin which provides a link to warning messages.
Different forums may treat violations differently, but personally I prefer corrective measures to be incremental so knowing how many times a violation has occurred is important. eg. (over simplified, but in general, similar to this)
- first minor violation - member gets a “friendly” message.
- first repeat of minor violation - member gets warning message if repeated within a relatively short amount of time after the first, else another friendly message
- second repeat of minor violation - temporary suspension
- third repeat of minor violation - long term suspension
tl;dr Knowing what the violation was, when it was, and how many chances a member has had to correct their behavior is important.