The SA scheme had some funky clock dithering. However, it wouldn't mess up approved military receivers, the dithering was actually a form of encrypted noise which could be removed by a receiver with the appropriate algorithm and key.
SA was actually disabled during the Gulf War because US troops didn't have enough military SA-decoding receivers (they started using consumer products, actually) and they decided it was hurting us more than it was hurting our enemy. Ironic since the entire purpose of SA was to deny accuracy to enemy nations during combat. One can't help but wonder why it was on in peacetime then in the first place. I have no explanation.
It was the FAA which requested that the feds remove the Selective Availability for navigation purposes. They're the ones who made it happen.
IMHO, it is unlikely SA would have lasted. I have seen no reports that SA was cracked in its lifetime, but nowadays, I would give it at most 6 months before some came up with an algorithm to crack it, feds threaten them with DMCA violations, court arguments happen, but the algorithm is loose and readily available to enemies of the USA while consumer mfgs for the USA are still living with SA's inaccuracies. Also Russia already launched a competing "Glonass" system and the EU has its own constellation planned. All that SA would result in is people abandoning the US's GPS hardware for systems without SA.
The GPS system can still be disabled or rendered inaccurate for a particular area. I suspect the military now has even stronger, secret encryption schemes other than SA that will make the signal read as garbage to any normal receivers.