You completely missed my point. As you say, the satellites all say "I am here (insert coordinates - 26,560km distance to earth center) and my local time is hh:mm:ss.xxxx", but how is that coordinate system defined?
THAT is the key question that defines how the coordinate system is "anchored". And since it relies on ground-based reference stations (though from Dare's comment it's sounds as though the stations are the active component there, and periodically update the satellites understanding of where they are), we must ask, how exactly do they compensate for motion of the stations? After all, there's no such thing as a stationary point on the surface of the Earth, everything is in a state of constant (slow) flux, as are the orbits of the satellites, thanks to solar wind, etc. Makes for a thoroughly squishy question