China has over 100 cities with > 1 million population. (113 to be precise).
The 100th-ranked US city (Huntsville, AL) has a population of 225k. (The 113th, Fayetville, NC, has just under 210k.)
San Francisco, with 808k population, would rank 126th in China. Not "small rural", but definitely a 2nd or 3rd tier city at best. (The comparable Chinese city, Anqing, is a prefecture-level city in the southwest of Anhi Province, and has, to boot, 631 years on SF.)
Consider that Wuhan, a city in China you'd likely never have heard of prior to early 2020, has a population of 11 million, more than any US city, and ranks 9th overall in population within China.
Non-major cities do, but not “small rural villages”.