Yes.
Peter by GPS computed you mean calculated by a fuel totaliser and displayed on the GPS right?
In the flightplan app I use for flightplan filing I can calculate the total time of flight. The app will take my average climb gradient, climb speed, cruising speed and filed flightlevels for all the enroute segments and calculate based on the forecasted winds-aloft. If I file e.g. 2 days ahead (which I never do anymore), then the calculation might be off and I get a push message telling me that the flight time calculation has changed based on new weather forecast information and thus I can adjust my flightplan. So far, the calculations were pretty accurate. OK, then in the Cirrus SR22 with Garmin Perspective Glass Cockpit I have the fuel totalizer giving me additional information while enroute. Together with the GFS model based forecast I have yet to encounter flights were the estimates were far off from estimates.
I described it partly here.
I have the same instrument but unfortunatelly it's not connected to GNS530 - obviously the guy who did panel upgrade didn't know it was possible.
What is the basis for GPS computed FOB? Does it use just GPH value you simply provide or it's connected to Shadin?
The Shadin transmits (about once per second) the current FOB and the fuel flow rate to the GPS, which obviously knows the current GS and the distance left to run so it knows the ETE and using the ETE it works out the Landing FOB. I think every IFR GPS has this function.
The gotcha is that the LFOB is obviously based on the current GS, which is dependent on the wind, so if you pick up headwind, the LFOB reduces. This is a parameter which I watch closely on long flights and if it fell below about 20 USG (depending to some extent on available/practical alternates) I would divert.
And obviously no good looking at the LFOB during climb. Sometimes it can be a negative value because the GS is so low 
No GA system AFAIK uses airdata i.e. current wind speed+direction to attempt to adjust the LFOB calculation for the change in GS due to later flight plan legs having a different track. But that's probably reasonable since the wind itself will change anyway, prob99.
However, in practice, the LFOB tends to be a suprisingly accurate prediction, from its initial value obtained at the start of the cruise segment.
I described it partly here.
GPS-computed fuel on board differed from the pump fill by just 0.36%.
What is the basis for GPS computed FOB? Does it use just GPH value you simply provide or it's connected to Shadin?
I have a Shadin fuel totaliser - system described here.
The accuracy is verified every time I fill up, and I always fill to FULL.
From my less than complete fillup records, this is a plot of the errors over last 7 years or so
The vertical axis is the discrepancy between the GPS-computed fuel consumed, and the pump reading after fillup, in percent.
Ignore the leftmost 5 values - those date back to before I fixed the installation bodges where (a) the transducer was in the wrong place (a Socata bodge - worth maybe 25% of reading) and (b) it was wired with unshielded cable which was picking up ignition noise (a well known Part 145 UK installer bodge - worth around 7% of reading). In those days the K-factor on the instrument was adjusted to take out the errors as best as one could, but the errors themselves varied a lot. The above writeup has more details. Those leftmost 5 values show the effect of the ignition noise alone. It wasn't possible to correct those by bodging the K-factor because the Shadin instrument has a gap in its K-factor settings right in that region...
Mostly the error is less than 2%, and on the safe side i.e. there was more fuel left in the tank than the system was showing.
The really curious thing is the pattern, which turns out to be roughly annual.
Looking back at the data, the highest "safe" values are during the winter.
2 possible reasons:
Avgas temperature coefficient of expansion (~0.1% per degC), and evaporation loss through tank vents.
The transducer measures purely volume flow (not mass flow) but so does the airport pump - doesn't it? So it can't be that. It has to be evaporative loss.
I can't explain the very occassional dips into the "unsafe" side, but I have found significant loss, up to ~ 1 USG i.e. ~ 4 litres per wing, after parking in say Greece (maybe +35C during the day) for a number of days. Since I fill up immediately after landing (for good reasons to do with airport working practices 
) this fuel is lost. 2 USG is ~ 2% loss. And indeed those spikes coincide with my longest summer trips to the south.
The 7% "good" spike (around #51) is the result of a bowser on a certain UK island airport whose meter is under-reading by 7%. I won't say where it is but anyway they have probably fixed it by now
It's a good system. For example, after landing from this long flight
the GPS-computed fuel on board differed from the pump fill by just 0.36%.
I recently talked to a police helicopter pilot at a birthday party @ friends who told me that they do not keep the reserves and fly until the fuel warning light comes on. Personally, I take fuel reserves serious and the last thing you want to end up with is being in a plane in the air without fuel.
Can you get prosecuted for something you said?
I am not a lawyer but I don't think so, because if they went after you, you could just say you made it up. Pilots often make stuff up
Anyway, "23 minutes" is nonsense. The only way you might know that is after you landed, and filled up from a known-accurate pump. And you won't find an accurate pump in Sudan I have a fuel totaliser accurate to 1-2% and it is "interesting" how the discrepancies get bigger the more south one goes.
If questioned I would respond that my statement about the "23 minutes" meant legal reserves plus 23 minutes.
Of course it is very difficult to check your fuel level. However if you request priority due to low fuel or something happens, you might get questioned upon arrival.
