In NYC, my experience with unlicensed cabs at airports is limited, but every time they did try to take advantage.

However, I had much more experience with unlicensed cabs in Washington Heights (north end of Manhattan, where licensed cabs refuse to cruise around to get business) and I never remember anyone trying to rip me off. Much of the time this wasn't with calling any specific company, just flagging down (illegally) whichever car was passing.

I think there's just too much money to be made from unsuspecting tourists at NYC airports.