yes, the cutoff for "urban" to not is 2000 housing units in an area. I don't consider that urban, 2000 homes is a decent "town". This is just "othering" of people who live more than 25 minutes from a metro which is what i consider "urban". i am 25 minutes from my nearest metro, and the metro population is smaller than the city i grew up in in california, population-wise.
my point is, talking about Berlin and then carrying that thought over to "americans just love cars" is silly. Germany is smaller than CA, and double the population of california. Most people "in california" live in the "san angeles" range or in the "bay capital" area. a half hour outside of any of those areas and it's either sand or farms or mountains.
and i wish i was "rural", there's ~600 houses within 6mi radius, that's not very rural. It's rural compared to Manhattan, i guess.
Without looking it up, I think it's also related to adjacency to a significant metro. But, yeah, the US census uses a binary classification that makes a lot of people assume "urban" means a big walkable city when, in reality, it often includes very dispersed exurbs (including places many would consider basically rural) that are never going to be serviced by public transit among other things.
So a lot of people tend to translate 80% urban into 80% cities which is manifestly not true, and even less dense cities.