Well I say "a lot of people" but its still a minority. Most people do stay in the city, live with roommates, etc. 30k people is an insignificant drop in the bucket compared to NYC's 8 million residents. On top of that, There are a lot of people who move into the city who already have established careers and have a well paying job lined up, or moved out of the city after college and then moved back after they've moved into higher paying positions.

On top of that there is a lot of international money moving into New York, as another commenter mentioned, and generally into the 2+br apartments with a family, further driving up the cost of living even with a roommate in the "safe" areas.