Okay, taking a look at the criteria they say they use.
Most of the weight is on research. Fair enough. I'm prepared to believe that conclusion, at least as an overall tendency. However, the context of the discussion was education, and that's the context in which I'm disputing the basis of the claim of superiority of American universities.
Of the fraction of the weight placed on quality of teaching, a significant chunk goes on 'perceived prestige' which obviously begs the question.
A small chunk goes on student/teacher ratio, which is a weak indicator; in particular, its behavior is more threshold than monotonic (i.e. you don't want it to be too high, but there's no real advantage in having it remarkably low).
And a chunk goes on total budget per teacher, which is a positively perverse criterion and tends to substantiate the stories I've heard about the level of waste in American universities.
So that's the 'world university rankings'. Moral of that story: when you see an official looking table that seems to support a controversial conclusion, look carefully at where the data comes from.