I think he meant tax rate not the percentage of total taxation paid by the particular group.
I've always been an advocate for a progressive tax scale, so you pay more at the margin the more income that you earn so that your effective tax rate continuously increases. The way the US system is set up at the moment, from what I've read and from that article, its seems its a mildly regressive system.
To me, this doesn't make a lot of sense, as the US has the highest concentration of megarich people in the world (thats a totally unsubstantiated statement btw). If you are the Government, why wouldn't you leverage that? Like Buffet says in the article, he paid ~6m in taxes last year, which equates to only 17 per cent of his taxable income. Right now, although I acknowledge I'm in Australia, I pay about 28 per cent of my taxable income in taxes. It just doesn't make sense to me.
If the tax scales were set appropriately, and exemptions and loopholes were fixed or tightened, I would expect that richer people would pay at least the same level of effective tax, not less.