Why a fake tower. The real towers can provide the same info with a simple warrant. Must be for more localized data. Unless these trick the phone into turning on GPS and sending that. Either way, if you connect to a network that's 2-way, the info you send back isn't something that you can exactly control.
In Canada there was a long period (maybe continuing today, not sure) where residents could not subscribe to satellite TV. There were methods that were available to get the service for free at the time. The satellite companies knew about this issue and wanted to correct it (the stealing service, not the unavailable subscription). The problem was, the signal is 1-way so they didn't have any way to track the pirates. Cable TV pirates are different though. Modern cable boxes are 2-way. As a result, it was possible to easily view satellite TV for free but go to jail for the same with cable TV. The point? Well, if you have a 2-way signal, you are at the mercy of your provider because they can really do whatever they want and you can't do anything about it.