All of this is true, but it's beside the point. The perception in America is that the rich pay more in taxes as a percentage of their income than the middle class do. The marginal tax rates imply that, with middle class people paying either the 22% or 24% marginal rate, and rich people paying at at 35%+ rate. Thus, people think that we have a progressive system.
However, if you look at the data in this chart, you can see it's not true any longer. The actual combined rate paid by most Americans is between 22-28%. (It's on the lower end for the poorest Americans, and for the wealthiest as well) Fundamentally, the total taxes paid is flat.
I think most people think that the taxes paid chart looks like what it did in the late 70s/early 80s. In that chart, the poorest Americans pay about 20%, and the richest about 45%. That's where we should be, instead of where we are now.