If Wikipedia is to be believed Boston added 18K people between 2010 and 2012. Between 2000 and 2010 it added 29,000. I think I also heard recently somewhere that in 2012 to 2014 Boston added another 10 - 15K people. The only thing I can think is Boston is being considered more than just Boston-proper but is including the entire Metro-west.
South Carolina has some weird outliers in terms of city limits and Greenville is one of them. The city itself is only 26.1 square miles and is mostly commercially zoned.
So while the data may show people leaving New York, it may not tell the whole picture. My own experience shows otherwise, though I am aware that anecdotes are not data. People may be moving out of New York City, but they aren't leaving New York City.
Here's an article from the same guys explaining the difference:
http://www.citylab.com/politics/2014/04/2-very-different-mig...
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.