One of the biggest issues is that the long term capital gains rate is only 15% (or perhaps 20% in some cases). It's likely that most of the taxed income of people with high net worth is from capital gains, and not from ordinary income. I'm not sure, but I think he's only talking about people with high ordinary income. He could be including capital gains too. Not sure. He's definitely ignoring high net worth.

The author does not directly address the low rate for capital gains.

Also, there are two ideas which are easily confused: 1) Do the rich pay more in taxes? Yes. The number of dollars Warren Buffet pays in taxes each year is more than his secratary. 2) Do the rich pay taxes at a higher percentage of their income? This article indicates the answer to this question is also yes. However because capital gains are taxed at such a low rate, and because of other loopholes, Warren Buffet's percentage tax rate is lower than his secretary's percentage tax rate.

Also, people with a high net worth do not have to sell stocks which have gained every single year. Maybe they sold some stocks a few years ago, and they are spending the cash. In the author's analysis, a high net worth individual with no ordinary income and no capital gains for this year would not be included in this analysis at all, because they had almost no income last year (probabaly a little interest and dividends, but nothing else).