They're his words (paraphrased) not mine, and it is impossible Buffet is unaware of corporate tax. My guess is its more than rhetorical flourish too since he's not known for that.
Your making the argument that corporate taxes reduce his personal income, and therefore should count as his taxes. Ok. But if corporations did not have to pay taxes, they would pay their employees more, including secretaries. It's impossible to say for sure that a 35% corporate tax rate reduces secretary salaries by 35%, but it is something highly significant.
In a roundabout way the secretary is paying that corporate tax too. Its effect is not as directly measurable on her as it is on Buffet, and might not be 1 for 1, but it's undeniably there and equally applicable to her tax rate.
Also Social Security reduces her pay by 12.4% (half of which is paid by her employer but again would likely go to her if not). Since its capped at $100k income, it rounds to 0% of Buffet's yearly earnings.
*I should point out that I am aware I've grossly oversimplified the effect of the corporate tax on the secretary, I trust but you get the point.