A lot of weight is indeed being put on the sat pings. I hope the engineers have thoroughly checked for latency issues or time stamp errors to ensure everything is as it seems. There are a lot of protocol levels in that system.
I am no satellite expert however I know that GPS satellite engineers adjust for the effects of the warping of space and time due to earths gravitational field. So looking at the contents of the satellite ping packet for a time stamp would be trivial for professional satellite engineers.