> But my current hypothesis is that many (most) Americans actually believe it.

I certainly believe that there is no rigid social class in America and it's definitely possible to move between income brackets with relatively little social stigma. In the UK for example no matter how much money a working class person makes they will never become upper class. Never be welcomed into the top social circles etc., they didn't go to the right schools (pre-college) or dont have the right accent...

I'm not as blind to believe that parental wealth doesn't matter hugely. I also wonder if it might be more difficult to move income brackets in the USA due to the extremely high cost of education.