You are right that COCOM is not the issue, but there are other measures.
The new military M code transmitted from the latest satellites is encrypted with a frequently changing key, so in the event of a war the DOD can disable the civilian signal as the M code will work standalone, hence a third party nation cannot rely on GPS.
The previous P(Y) code was also encrypted, but is theorised to need the civilian C/A code as well to work.
> so in the event of a war the DOD can disable the civilian signal as the M code will work standalone, hence a third party nation cannot rely on GPS.
They also had the option in older satellites of turning on selective availability, which would degrade the civilian location service from 5-meter to 100-meter accuracy without affecting the military service. Purportedly newer GPS satellites don't have the option anymore.
Selective availability was defeated a very long time ago so no reasons to doubt that the military gave up on it. Pretty sure they're just using an encrypted transport for the military signal so they can do whatever they want to civilian GPS wholesale without impacting the military. However, I'm not sure how that will work since it underpins our entire economy from logistics to air travel. On the other hand, at the point the military is disabling civilian GPS probably the economic impact is less of a concern.
It's worth mentioning here that SA-less Block IIF (and newer) satellites came after "codeless" and "semi-codeless" techniques were publicly-known. Those allow a receiver to use the encrypted P(Y) code to obtain a precise position fix without any knowledge of the encryption key.
There are probably other, newer ways to prevent an adversary to use the GPS signal, but there is little reason to doubt that SA is gone.
https://en.wikipedia.org/wiki/CoCom#Legacy
Edit: I'm wrong.