You are right. The military relies on INS and GPS. Most systems such as the navigation in an F/A-18 are INS with GPS to maintain accuracy like you described. I thought JDAM was entirely GPS, but apparently it is only an INS supplement to.[1] Cruise missiles use both plus terrain mapping.[2] Military could probably handle total GPS denial, but it would be ugly, especially since it may mean no SATCOM either. I ponder what WW3 looks like and total space denial seems like a strong possibility. Spoofing is probably worse than denial since it isn't just no information but bad information that could throw off the INS.

[1] https://en.wikipedia.org/wiki/Joint_Direct_Attack_Munition [2] https://en.wikipedia.org/wiki/Tomahawk_(missile)