GPS and similar systems are just big atomic clocks flying around the earth, shouting their time down to earth. A GPS (or other) device just needs to know the current time and the position of the satellites to calculate its own position.

The most control the US ever exercised over GPS was to encrypt the more precise parts of the satellite’s timestamps so that only military devices could get really precise positions. They stopped doing that when other systems went online. That was for the whole world, including its own citizens.