That is not correct at all. How did you arrive at that conclusion?
GPS has its own independent timescale called GPS Time. GPS Time is generated and maintained by Atomic clocks onboard the GPS satellites (cesium and rubidium).
I think GP might’ve been referring to the part of Jeff’s post that references GPS, which I think may be a slight misunderstanding of the NIST email (saying “people using NIST + GPS for time transfer failed over to other sites” rather than “GPS failed over to another site”).
The GPS satellite clocks are steered to the US Naval Observatory’s UTC as opposed to NIST’s, and GPS fails over to the USNO’s Alternate Master Clock [0] in Colorado.
[0] https://www.cnmoc.usff.navy.mil/Our-Commands/United-States-N...
It has its own timescale, but that still traces back to NIST.
In particular, the atomic clocks on board the GPS satellites are not sufficient to maintain a time standard because of relativistic variations and Doppler effects, both of which can be corrected, but only if the exact orbit is known to within exceeding tight tolerances. Those orbital elements are created by reference to NIST. Essentially, the satellite motions are computed using inverse GPS and then we use normal GPS based on those values.