They only need to change the CDMA codes of the civilian GPS to render it unusable. Also at the beginning of GPS they purposely added inaccuracies into the timing to make it less precise for civilian use, but because of the FAA and other needs (and methods that have been developed to counter the injected inaccuracies) they finally removed it in 2000.

To respond to my question. With long term measurements and the help of the L5 band it is possible to obtain sub-millimeter accuracy [1]!

[1]: https://en.wikipedia.org/wiki/Global_Positioning_System