Note that Iran captured a RQ-170 drone back in 2011, possibly using GPS spoofing, so obviously using the encrypted military GPS signal isn't a perfect solution.
https://en.wikipedia.org/wiki/Iran%E2%80%93U.S._RQ-170_incid...
(How did they do it? Who knows. Maybe they jammed the encrypted channel, and spoofed the civilian channel, so when the drone fell back onto the unencrypted channel it was receiving bad navigation information)