That stereotype used to have a lot of merit. In the latter half of the twentieth century, in the aftermath of WW2, America was teeming with newbies from whereverthefuckistan who were at best half-integrated, and who were making serious moves in spite of barely having arrived. That “land of opportunity” mythos was entirely real in this period and people took that idea seriously.
So of course people under the boot of communism went starry-eyed when they saw national propaganda to the effect of “welcome to the concrete jungle, it’s NEW YAWWWK CITTTYYYY,” especially when that shit was about 75% correct unironically. It’s only later on, like in the 2000s onward, that this really started to erode.