My lord you people are beyond patronizing.
When people refer to "the Chinese" or "the Russians", we are taking about the nation state, not the people. And there are legitimate security concerns. Whether we should be adversial is another question. But we are.
I think US is very tolerant when it comes to people from Russia.
You said, "ask a random stranger...and he will honestly say no" not "ask a random stanger...and he will probably honestly say no".
Most of most people are racist, it's just different groups. Americans obviously have less distrust of americans, but then I am just as certain that there are many many humans who would proudly share their "dumb american" stories as if that is not every bit as prejudicial to those of us who do not fit the description as any other "weak french" or "commie russian" or "sister fucking indian" or whatever else.
Racism is about race (i.e. phenotypical or genotypical properties), while being US-American/French/Russian/Indian/... is about nationality. So, these stories are not about racism (since they are not about race), but about prejudices against other nations/nationalities.