Turing off GPS would not have to be binary. There is a seperate, encrypted, GPS frequency that the US government can continue using even in places that they shut down GPS for everyone else. Additionally, they can degrade the accuracy of civilian GPS (also in a targeted area if they wanted).
During the Iraq war everyone kept trying to find these magic encrypted GPS devices that used military only frequencies. I never saw one, or heard of anyone using one.
Even SEALs are issued the same Garmin Foretrex 401 you can get at Best Buy.
I believe that they're considered classified material and are also big, clunky and expensive, which is why the military just ends up using standard civilian GPS equipment a lot of the time.
Government fab and production tech can't compete with the stuff on the open market. From GPS to crypto hardware, civilian stuff is almost always smaller and more usable. I suspect most hardware using the encrypted GPS channels is in munitions.
A GPS receiver is not supposed to work at an altitude greater than 60000 feet or while travelling at over 1000 knots, but the system itself does not in any way enforce this restriction [1].
A friend in Houston was telling me in the early 2000s about working on a NASA JSC project to use an off the shelf GPS receiver on the space shuttle. It took a few iterations on the firmware to handle 18,000 mph, etc., but he said the vendor eventually converged on firmware that worked in orbit.
To be clear, it's not that a receiver couldn't work, but that it shouldn't.
A civilian receiver is meant to deactivate under certain conditions lest it be suitable for use in things that go very fast and fly very high, e.g. missiles.
So as you say, you may be able to change the firmware to disable these restrictions, just don't try and take them out of the US...
