I think that depends on your definition of "just about." Every borough in NYC aside from Staten Island is much denser than San Francisco. Additionally, many parts of where I'm from – northern NJ – are even more so: Hoboken, West New York, Union City (the densest city in the country), Guttenberg (the densest township in the country), and more.
If you're talking about cities larger than a certain size, then perhaps, but even then, I personally think it's a bit misleading to single out just Manhattan.
This is why having fast rail, uncongested highways, and always expanding to meet demand are always worth the cost. Unless you can accurately forecast a downturn in regional economic growth irrespective of whether or not you meet transit demands, it is never rational from the perspective of long term city planning for maximum economic throughput to not grow the system and increase density.