All systems have separate channels for public and military use, as well as SA capability (of the public channel), as well as the channels can be switched off/on anytime. I can hardly imagine how you would limit its usage in certain areas like a "border of a state".
The SA does not work such the public service will not be available to a certain state or entity, but it dithers the signal such the precision goes down from say ~10m to ~100m. That is all. US had switched SA on many times on the public channel in past and nobody from public sector noticed that, afaik.
The military channels are not subject of the SA, of course (as you cannot decrypt them with cheapo devices we all use).
SA is there to avoid the situation Dr.No would put his $20 phone with GPS into a rocket he will shoot and navigate against James Bond's yacht.