I'm glad you're OK. Many doored cyclests are not. There's more you could have done besides being paranoid about stopped taxis. You should have taken the cab's number and reported the incident to the City's Taxi and Limousine Commission. That would have made the cab driver paranoid about discharging passengers in an illegal manner.

The cab driver was at fault. There are locks on the passenger doors that are controlled by the cab driver. He should have prevented the passenger from opening the door. NYC Traffic Rules are very specific regarding where taxi drivers may discharge passengers to wit Section 4-11 of NYC Traffic Rules

(c) Pickup and discharge of passengers by taxis, commuter vans and for-hire vehicles. Operators of taxis, commuter vans and for-hire vehicles may, in the course of the lawful operation of such vehicles, temporarily stop their vehicles to expeditiously pick up or discharge passengers at the curb in areas where standing or parking is prohibited. Taxis, commuter vans and for-hire vehicles, while engaged in picking up or discharging passengers must be within 12 inches of the curb and parallel thereto, but may stop or stand to pick up or discharge passengers alongside a vehicle parked at the curb only if there is no unoccupied curb space available within 100 feet of the pickup or discharge location; however, picking up or discharging passengers shall not be made:
(1) Within a pedestrian crosswalk.
(2) Within an intersection, except on the side of a roadway opposite a street which intersects but does not cross such roadway.
(3) Alongside or opposite any street excavation when stopping to pick up or discharge passengers obstructs traffic.
(4) Under such conditions as to obstruct the movement of traffic and in no instance so as to leave fewer than 10 feet available for the free movement of vehicular traffic.
(5) Where stopping is prohibited.
(6) Within a bicycle lane.
(7) Within horse-drawn carriage boarding areas.

From your description the taxi driver violated at least two provisions that allowed him to discharge the passenger more than 12 inches from the curb - items 4 and 6.

The NYC Council is currently debating a series of bills under the Vision Zero umbrella. Several are designed to make taxi drivers more responsible for their actions. Taxi driver representatives are claiming such legislation targets them unfairly. They are also claiming they are among the safest drivers in the City. The best way to counter their assertions is to make sure that no transgression goes unreported.