Sounds like one of those "what if..." things someone made up.
AirTags are terrible for surreptitious tracking, alerting every iOS user nearby of a tracked product following them around.
I mean, years ago people, such as stalkers, would use it for this purpose, but Apple rightly gimped that. There are a lot of specialized, self-connected trackers that creeps and criminals use.
I've only been notified about a device traveling with me one time, and it was when a relative was riding home with me in my car. When we got home, I received a notification that there were AirPods Pro traveling with me.
This is consistent with my understanding that it only goes off if it travels with you for a very long time, or to your house. (Of course, at that point it's too late because they know where you live already.)
Well, to be historically accurate: Apple has pretty much been forced by the backlash to notify people that they're being tracked and even then it only worked if you had an iPhone.
They knew what they were doing and I'm sure the stalking aspect helped their sales significantly as it seems to be a very popular behaviour in the US.
And simultaneously gimped the theft-alert use case. I embedded one into my labelmaker, which is a notoriously high-theft item on jobsites. I can still track it in case I leave it behind, which is great.
But if someone steals it, they get an alert that there's an airtag traveling with them, and they can go through their loot to figure out which item it is, and ditch it, or destroy it. In the first case I get my labelmaker back, but I never bust the thief.