Comment by pizzly

In theory it could. Usually there is accelerometers on them so they can definitively measure this. The tricky part would be determining if the phone belonged to the driver and which car is being driven.

You could properly infer if the phone owner is the driver by determining if they use the phone less than the other car's inhabitants or if they are the only phone detected driving at that speed and location. Or they use the phone more during traffic jams and less during more intense driving.

Then this leaves determining what car is involved. You could potentially see if the phone is connected to the car's entertainment system. That would tell you what car model it is perhaps even with a unique car id though the serial number. Some cars may have bluetooth/wi-fi and the phone could potentially passively scan the largest most consistent signal to get the car's model without ever connecting.

Cross referencing from other data sources (cameras) would give this information though may still be difficult/expensive/unlawful.

So in response to your comment its possible that the chosen surveillance device does actually report acceleration events to LexisNexis and then Progressive. Or this is is a case of overly being paranoid. Either case the possibility exists.