In Washington, DC, taxicabs used to charge via a "zone" system - it didn't matter how far you went (necessarily) - the city was divided into multiple "zones", and the rate was charged based on how many zones you had to travel through to get to your destination.
People (particularly tourists) complained about this system because it didn't make complete sense and a tourist, or even just someone not familiar with the zone map, wasn't going to be able to look at the map and see where the zone boundaries were. As an example, if I was in a hurry, I could take a taxi from my home, to work. The total was 3 zones (with a minimum, of course, of 1). However, if I walked 1 block south from home, hailed a taxi, and had it drop me off 1 block north of work, it would be 1 zone. That would save a good percentage of the cab fare.
However, a tourist getting in the car would have no idea - furthermore, if a tourist was being dropped off, say, right near a border, if the cabbie says "Hey, traffic is bad here, mind if I drop you off across the street?" most people would say "OK", figuring that in most cities, that's probably nothing, or maybe an extra quarter or so. In DC, it could be an extra $2.
A little over a year ago DC switched to a metered taxi system, as mandated by Congress. Prior to the switchover, taxi drivers in DC went on strike, saying they'd lose significant money in a switch, despite the fact that the rates were set such that the average metered trip would actually net more for the driver than the old zone system would - but only under the assumption (which the people setting the rates were using) that the zone system was being used fairly and customers were not being diverted, sometimes only short distances, in order to add zones (sometimes, near zone borders, moving a few blocks could be two extra zones!).
You'd get a constant circle:
Taxi Driver Committee Representative: "We'll lose tons of money switching to meters!"
Taxicab Commission: "But under this new system, a driver would actually be getting more money on an average trip than before, unless they were routinely cheating customers in a way the new system would prevent. Look, we'll open the books to you, examine the whole thing."
Taxi Driver Committee Representative: "Ah. I see. We, of course, have never cheated anyone. But notwithstanding that, we'll lose tons of money!"
The change took place anyway, and the world hasn't ended, although the data does seem to reflect that cabdrivers are making less than before, yet somehow the data also shows that they're making more per trip than before. How? Because before they were manipulating the system to charge more.
I doubt this is any different. Most people in the cab in NYC aren't going to notice if the fare is $X or $X+4, unless they're a native. Just like I could tell my cabdriver in DC "No, drop me off here" whenever they tried to move an extra block near a zone boundary, a native might catch it. But someone unfamiliar? No. Thus, I'm going to side with the GPS on this one.