This does not follow. The US Navy uses very high-precision inertial navigation systems, networks of them embedded throughout the ship and measuring position independently in fact (think wisdom of crowds). External corrections are only accepted within the very small aggregate drift error. Spoofing GPS will do almost nothing to a US Navy ship, that isn't how they navigate. Hanlon's Razor applies.

The US military is very, very good at exotic inertial measurement technology, doubly so for a platform like a ship with few power/weight limitations. It is a cornerstone of their technology advantage.