David Leonhardt: The rich hide their income from the IRS, but the poor don't

In an otherwise relatively informative column, David Leonhardt makes an assertion that I don't think holds water:

If anything, the government numbers I’m using here exaggerate how much of the tax burden falls on the wealthy. These numbers fail to account for the income that is hidden from tax collectors — a practice, research shows, that is more common among affluent families. “Because higher-income people are understating their income,” Joel Slemrod, a tax scholar at the University of Michigan, says, “We’ve been overstating their average tax rates.”

Is he really claiming that, proportionally, the rich hide their income more than the poor? Aren't the poorest of the poor the most likely to be earning their income from under-the-table (or even outright illegal) jobs? Literally every person I know on welfare (be it 3+ months of unemployment, or food stamps) also currently (and often) has a significant second source of unreported income.

Sure, very rich people have off-shore bank accounts and accountants who fix things so that they pay lower taxes, but the average person earning $150k+ isn't getting large amounts of unreported income. The average person reporting less than $15k in yearly income, on the other hand...