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Alex,
I need to read what's there carefully, it will take some time for me to devise the accurate reply (because it will have to involve some more complicated math... ).
For the start, we can say the following:
In mobile phone, signal processing block does something called "derotation" of the received signal before de-coding into useful data.
Basically this is frequency sync with base-band signal, so the decoding could become possible.
I suppose the similar technique is used at GPS receiver-- so there is no need for atomic clock in mobile phone, and yet it is still possible to have the same timing accuracy as there was one present.
As you know, atomic clock uses electron orbitals energy level diferences as time base for its operation.
Due to GR, it runs faster in orbit compared to the one running on Earth surface (this is the fact, confirmed independently from GPS).
Also, Doppler effect plays the most significant role in positional accuracy.
I think the correction needed for all the above to achieve the required GPS accuracy of the position is not so simplistic as suggested by the website you linked.
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