If it was true, US cities, the high density areas, would have speeds comparable to countries such as Estonia (12mbps), Japan (50+mbps), and so forth. However, US internet sucks, even in the cities. In my experience there is almost no correlation between density and quality of internet. And don't make the argument that it's due to the distance between cities: fiber trunklines cost almost nothing compared to the last-mile costs of wiring thousands of neighborhoods.
What is true is a correlation between competition and quality of internet. Areas with only one provider almost inevitably have terrible service.
The excuse that "US internet is worse because our country is larger" is a cheap cop-out to avoid admitting that our telecommunications infrastructure is in many ways worse than some third-world countries.