I'll start by saying I am not a good tipper. I will tip very well in circumstances that go above and beyond but it must be well above and beyond what is expected in my eyes.
In this case (or similar cases where the tip is precalculated or set somehow) I automatically tip less when getting the service that I think I paid for in the fare, food price etc.
Restaurants are a good example
$25 food charge
$1.50 tax
$26.50 total
tip line
and it lists suggested values, 18/20/25%
I will default to 15% and round down just because they did this and what irks me even more is that they calculate the tip on the amount including tax; they didn't earn a penny due what is billed as tax
I also am one who leaves a cash tip even when paying with a card whether its a restaurant or cab
I don't have a problem with what the OP did to the cab driver although I probably do give him $8 and make it an even $60 but I never pay till I get my bags out of the car. I just don't trust them even more so in a city like NYC