IIRC, this indicates that it's linked to someone else's account, and has not been shared with you. The "beep when moved" feature is to alert people they're being tracked.
For example, I let my mother in law use luggage of mine with an airtag still in it and every time she moved it after the first day or so, it would play a noise.
I had the thought too, but there is no way anyone else could have gotten physical control over this and shouldn't I see that AirTag when I scan for things in my surrounding as an anti-tracking protection?