I would be extremely surprised if that was true. Even if you count not having to own a car or commute as long-distance in New York. I live in a 1 bedroom apartment that is 2550/month and _everything_ is more expensive here. A bottle of wine that might cost $9 in most places is $14 here. Bars and restaurants are far more expensive than they are elsewhere in the states, and city tax kills me to the tune of around $800/month.
Rent prices have reached about par according to padmapper.com. Mountain View, a somewhat shabby and boring suburb, that wouldn't be costly if it wasn't for SV, is the same price as brooklyn.
Amazon Prime pretty much removes most of the price and sales tax inequality.
The tax difference is real. But then again, the tax difference compared to austin or seattle is also very real too.