I'm not American; I don't know the tax structure. But I can't even imagine that this could possibly be true, or what is true that is meant.
Without looking it up, I would assume that the USA subscribes to progressive taxation, under which the richer pay more tax in both absolute and relative terms.
Even if it has a flat rate of tax, (a structure, incidentally, that makes far more intuitive sense to me) the richer are still paying more tax in absolute terms, and equal in relative terms.
What Earthly metric is the author using?