The Navy is historically in charge of keeping official time in the US, and many other countries. It's not that they can or can't make adjustments vs any other

The Navy is historically in charge of keeping official time in the US, and many other countries. It's not that they can or can't make adjustments vs any other standard of keeping time, it's that they don't have to. Whatever may (or may not) make sense today, we adjust to Navy time, because that's what's official, and that's what GPS time is ultimately based on. Re, relativistic corrections, I don't know the answer for sure, but they average the time between multiple (I think cesium?) atomic clocks. If those clocks all shared the ~same reference frame, I'd think, by definition, you'd not need to make a relativistic adjustment. The frame you'd reference to is the one you're already in.