Maybe it was the tone in which the interviewer responded, but that statement just seems like a reinforcement of the fact, NYC is expensive.
I have a hunch this person has received many complaints from previous people who might have held this position or other positions at this pay grade, and want to underline the fact it will be a challenge to live in NYC on such a salary. They want to be able to say when you come back into their office to complain about the pay during the course of the job, they can remind you they warned you. I think that perhaps young, starry-eyed stage managers are so eager to land in NYC with a job, they want to protect themselves.
But I may biased, mostly because “Yes, but saying you can live in New York and doing it are two entirely different things.” Seems like an understatement to me.
I think you handled it the best way you know how. And remember, part of a good interviewer's job is to try to throw you off balance, get you off your rehearsed speech, and get to know you. This may have been a curve ball.