.. But the modem itself is broadcasting it's identity to multiple radio receivers. Is there enough of a difference wrt GPS positioning for the distinction to matter?

Sure, I agree it’s subtle. But it is: a) much higher resolution b) potentially to a specific third party who may not have access to cell network data. Like, say, an angry ex-spouse.

Aha! That is a valid concern indeed. Lesser than the usual "baseband has full access to whole system", but still significant.