Not with the latest block of satellites. They are capable of inter-satellite communication, which means, very theoretically speaking, a call between two Starlink users could be completed without ever touching the ground, apart from the two customer endpoints of course (in other words, no ground station need be involved).
I wasn’t aware that Starlink allows mobile customers as yet, at least not in my country. Maybe it is being trialled in the US.
(So the implication is that your location is fixed permanently and hence known - just like a fixed line phone or a cable service. Worst case, the customer satellite dish hardware has a GNSS chip in it. Best case, it is not actually enforced right now at all. Middle case, the satellite system is checking that your location as recorded and disclosed is inside the beam footprint of the satellite that you are currently communicating with and LOS/AOS could even be used to confirm that more precisely.)
I would put my opinion this way: Elon will be pursuing Elon’s interests. If they align with yours, lucky for you. If they don’t align with yours, unlucky for you.
I’m pretty sure that sooner or later the US government will “explain” to Elon how cooperating with the US government is in Elon’s interests. 