The claim is correct for relative income and incorrect for absolute income. In absolute terms, wages have been stagnating for a long time and combined with technological progress, yes, absolute real wealth may have advanced for almost everybody. The problem is, people define their incomes in relative terms, and with the total excess at the top management levels since the Soviet downfall combined with mass media, most Americans have been suckered into debt. So I would venture Americans' net-worth has indeed declined long-term, even absolutely.
Real wages purport to measure the amount of stuff one can buy, not the income as a fraction of some richer person's income. The claim I'm disputing was made about real income.