US, but the claim wasn't "selected portions of the most dense cities in the US". It was "Our population density (in the United States) is very high as it is in, most metropolitan regions."
I don't doubt Manhattan is very dense. It is far from representative when it comes to "most" metropolitan regions in the US.
The same distinction applies to the population density of various Amsterdam "boroughs" (or satellite districts) whether its Almere or Bos en Lommer. The density & the people you run into varies markedly although they're both accessible by public transit and are only a stone's throw away with what you typically associate with Amsterdam.
How is commuting in from Zwolle or Amersfoort to Amsterdam Centraal different than say commuting in from New Canaan, Connecticut to Manhattan?
I'm sure the same is the case with any large metropolitan region anywhere in Europe.
I don't doubt Manhattan is very dense. It is far from representative when it comes to "most" metropolitan regions in the US.