Wrong. It's a /p cache. Saves the server a bit of effort from having to constantly query the database. Not entirely sure how long it caches for. I'd guess 15-20 as I mentioned this to JackBiggin last night, as after he left, /p said he was still online even 15 minutes after his disconnection.
As Fate said, I believe there is a bit of a bug with /p, I believe staff were made aware a few weeks ago