Why? Two reasons given 1] Her husband might show up any minute. 2] The very fact that her husband is in town makes her uncomfortable enough to ensure that their will be no monkey business. [Lamdanim - What's the nafka minah between the two taamim??]
A question I have long wondered about - What is considered a city? New York is awfully large. All of New York is one city? I'm in Manhattan and my wife is allowed to have Yichud in Flatbush? That's awfully far away. Also, let's say I'm in Bnei Brak and my wife is NEXT DOOR in Ramat Gan [more likely]. That's considered another city and she's forbidden in Yichud?
So the achronim argue: Some say that indeed it all depends on what people call it. If here is called Bnei Brak and next door Ramat Gan yichud is forbidden. But Flatbush and Manhattan are both called New York City so it's cool.
Others hold that as long as you have one stretch of houses that is enough to be considered one city. So in the next door example it would be permitted.
Li'halacha one should ideally be strict like the first opinion.
Now, the poskim don't discuss different boroughs. I would suggest that people generally call Brooklyn "Brooklyn" and Queens "Queens" and not New York, so MAYBE they would have the status of different cities and hence the hetter of baala ba'ir would fall by the wayside.
It is important to note that ideally one should not rely on the hetter of baala ba'ir at all. Many feel the gemara was only permitting it ex post facto [בדיעבד in French:-)]
We have heard bad stories even when baala ba'ir....
אין אפוטרופוס לעריות say the sages. The nature of the human animal is that when it wants to do something - it finds a way.
