The drunk who lost his keys up the street, but is looking under the street lamp because the light is better there comes to mind. There is a human propensity to look at what we measure and forget all the impact that our actions may have had on changing measured values. We changed tax rates since '79, and we famously lowered them again in '01 -- surprise, the REPORTED income equality went up in each case.
One way of looking at REPORTED inequality is that when tax rates on the wealthy are "favorable", they will actually report the income and pay the tax. When the rates aren't, the business will buy another truck, retain the earnings, etc, or the person will take some of the income in stock, insurance, invest in tax free bonds vs stock, etc.
Being rich, like being heathy, presents one with more options. In my mind, by definition, if you are rich, you don't HAVE to work -- but if the taxes are reasonable enough, you may decide to do so.
The larger truth is that recessions always destroy wealth and small business incomes at the top. Perhaps those who obsess over income shares should welcome stock market crashes and deep recessions because such calamities invariably reduce "inequality." Of course, the same recessions also increase poverty and unemployment.