Corporate tax rates plus capital gains tax rates exceed normal income tax rates. The only way you can claim that he pays less in taxes on selling stock is if you assume that the company's profits -- the sum of which, discounted to the present, is the value of the stock -- somehow don't affect the value of the stock.
If we cut capital gains taxes to zero and added an equivalent amount to corporate profits (say, a 40% annual tax rate instead of 35%), the government would make an equivalent amount of money from the same economic activity, and Buffett's theoretical tax rate would go down. Similarly, if corporate income taxes were zero and his capital gains were taxed at 40%, he'd pay much more than his secretary, but the government would collect the same amount.
If the strength of his argument is independent of the magnitude of the problem he's arguing against, there is a flaw there.
Buffett is an admirable guy. But the line about his secretary is a rhetorical flourish, nothing more.