It should be no surprise that Buffet pays less tax than his secretary in a "progressive income tax" system.
"Progressive income tax" is not the root cause for Buffet's Secretary Syndrome.
Buffet's Secretary syndrome is one example of how the wealthy have skewed the rules of the game in their favor. Progressive taxation would go part way to mitigate the problem.
Granted, the complicated tax exemptions written into the law are a big part of the problem. Who do you think were the architects of that, the poor or middle class?