You're right, it is a false choice. But before we get to discussing that, we should first be considering whether there's a choice that needs to be made at all.

I personally am far from convinced that law enforcement has a significant problem with locating fugitives. I may be wrong with this, but I haven't seen anything concrete to dissuade me from those views. How often are such location services actually needed, and what are the consequences of not having them available?