I can confirm that last bit: I've used the GPS (with a good fix) without running gpsd, libgpsbt or libgpsmgr, and in that case /var/lib/gps/gps_last_saved_report does not get updated. But apparently this file is only used for the UI...

Jukka R. explicitly stated that gpsd timestamp is not fed to the chip, so I'd say that's ruled out. But he also said "almanac and ephemeris are fed back to the chip", somthing I wasn't sure about earlier (the chip could have had an internal memory, although I guess that's unlikely).

Ephemeris data has to live in /var/lib/nvd_data (That's the only file I see getting updated with the setup mentioned above). ag2, are you familiar with almanac / ephemeris data? Does the size of the file look like it's in the ballpark?

The data structure seems variable so the following could be different each time.... The file I'm looking at has two digit hex numbers in six groups, padded with zeros in several places:

1: 3457 numbers (everything after 752 is zero)
2: 1153 numbers
3: 25 numbers
4: 35 numbers (mostly zero)
5: 73 numbers
6: 25 numbers