If you are discussing a specific event / user, then don't post on MSO; use the flag for moderator, or e-mail the team.
If you are having general discussion about user-interaction, then MSO with the discussion tag should be fine.
It is interesting... and indeed "we" have recently been discussing (off-forum) how we handle moderator collaboration. Thinking aloud, the problem with just a flag or tag (with an access check) is that even if it is impossible to get it wrong there would be a lot of places to check that the data isn't being exposed... which could be painful
- data dump
- "new post" outputs
- user stats page
- auto-suggest when asking questions
- "related" panel
- ?does the captcha use text from the site?
- 10k rep "tools" pages
So I'm not sure that a regular question (with a flag) is the safest option if privacy is important. I'm not convinced that we see enough of this to make it really necessary to do much extra to secure it (against the above). In most cases a moderator flag will get our attention, with the e-mail as backup (and for longer questions).
Or another way: is there a specific scenario you want to "fix", that doesn't work (well) with the existing processes?