Practically speaking, high taxes are not an effective way to tax the wealthy, but they are an effective way to send capital overseas. If you want another example, look at the $2.1 trillion in U.S. corporate cash being held abroad, which hasn't been repatriated because companies refuse to pay the high U.S. corporate taxes, and use it to buy foreign companies/assets like Minecraft for a couple billion instead.[0]
[0] http://www.bloomberg.com/news/articles/2015-03-04/u-s-compan...
So how are they effectively paying the lowest band?
If you make 1 million dollars per year, and I make 100k, and my taxes are 30k per year while yours are 100k/year (numbers made up), you'd be paying more total taxes, and a larger slice of the total tax dollars paid.
However, my taxes are 30% of my income, whereas yours would be only 10% of your income. If we paid at the same "band" of taxes, you would be paying $300k instead of $100k.
Because the tax bands tax you at a lower percent the higher up you go, making more money leads to less proportion of taxes.
Consider also that the people who pay the most tax (in dollars) often have a substantial amount of their wealth in real estate, stocks, or stock options, rather than cash income, and those are all taxed differently than the kind of income that most of us have.
And thats at the federal level. State income taxes vary from place to place, but nowhere is what you are saying true. And a state would have to apply a substantial effective negative income tax rate for high earners which is laughably unheard of.