When doing a base pick up they have a flat rate like any other livery car. Pretty much green cabs are livery cars with the ability to pick up on the street. Livery cars and black cars are not allowed to pick up street hails, even though most livery cars pick up anyways.
The "no meter" part is because a great deal of people in low income neighborhoods don't like the meter, they perfer a flatrate. They don't like the uncertainty of the price when it comes to the meter.
I remember driving yellow and always have people complain that the meter is moving faster than usual. I used to calm them down by giving them a pretty good estimate on how much it was gonna come up to