Much of the myth is tied in to Americans attitudes about work. It defines who they(we) are much more than in Europe.
An Italian friend described it this way... " Americans live to work. Italians work to live".
He said that taking a few hours off to lunch or nap during the day would not raise eyebrows in Southern Europe especially....but in the US it would be unheard of.
I much, MUCH prefer the European way.
But (many ?) Brits don't like to think of themselves as "Europeans" (see Brexit as a case in point). Furthermore, Italians are different from Germans, or Swedes, or Dutchmen. In fact, I can tell you from personal experience (my family is part Italian, part Portuguese and, in a very smaller part Spanish) that even southern Europeans are not equal to each other (for example, the Portuguese have a fairly different culture from the Italians and the Spaniards). And I am not even getting into Eastern Europeans like the Poles, the Czechs or the Hungarians.
Bottom line, I don't want to get into an argument which may turn political (because of Brexiteers on one side and EU-enthusiasts/Eurofederalists on the other), but "European" is actually an artificial concept that is sometimes used to describe 400 million+ very diverse people.
Finally, I also take the claim that "Americans live to work" with a grain of salt. As I see it, many Americans work longer hours than in some other countries or have multiple jobs because, quite frankly, live is tougher in the US than in other advanced economies due to the lack of a proper social network or welfare state. So many people have to work harder to have a decent living. I also think it is fair to say, compared to other countries I know, that the American workplace is more competitive/brutal and that Americans tend to be culturally more driven by ambition or a desire to be "successful"in life (also because, again, not being a social-democratic country, it is harder to be a "loser" or just mediocre in America).
On the other hand, however, there are things that strike me in America. I went to Graduate School in a STEM field and I can say that, over 50 % of the PhD students were definitely born overseas (mostly Indian and Chinese, but some Europeans, Russians, Middle-Easterns and other Asians too). And then there were American-born kids who were first generation Americans (again, many East Asians and Indians). There may be more traditional WASP Americans in more "lucrative fields" like Business or Law school, but it surprises me how many young people in those demographics shy way from "hard science" and engineering careers. Does that mean American students are "too lazy" for science or math?
Anyway, I won't go any further because I am obviously off topic. It is just that this attitude of assuming Meghan is somehow superior to the Palace staff because she is American and they are lazy Brits irritates me somewhat.