Take the following chart, which is supposed to show the relationship between one's wealth and the share of income taxes he or she pays. Piketty's intention was to emphasise the scandalous fact that the poorest pay a bigger share of their income than the richest. See the green line.
After adjustment for several factors, including unemployed and students who pay no taxes at all, income after redistribution, and non-existent income such as non-distributed corporate profits or imputed income from real estate, the final relationship appears much less scandalous. See the blue line.
The fact that the lowest income decile pays a higher share of taxes that the third decile is odd, but not exactly a cause for a revolution. Neither is the fact that the super-rich pay slightly lower share than the “ordinary” rich.
Knowing an important piece of fact like this, would you believe Piketty's book any longer? Or would you wish to get your money back?