The problem here is we are all making educated guesses. I don't think there is anyone posting on this site who knows the exact logic of the feeds to the TANS on this particular aircraft.
If the equipment was fully sericeable, statistically:
1. The GPS position would be good to a few metres.
2. The doppler position would be about a mile away.
3. The ADS position would be 1-2 nms in error. (Assuming forecast W/V had been fed in.)
Operating the TANS in either reversionary mode is preferable to swiching it off, because the Computer takes all TAS and Heading variations into consideration. Something Heading Airspeed Timing does not.
If the crew were having problems with the TANS, the first port of call would be SELECT DOPPLER (or ADS with W/V update)
Switching off would be a last resort. Yet the crew (apparently), switched of a fully functioning TANS while approaching a cloud covered headland at high speed.
Does anyone on my planet think that is a logical explanation of events?