This is correct if you consider "better standard of living" to mean "better standard of living relative to rest of the world". In terms of actual consumption and productivity, young people in America will have far richer lives then their parents, because the exponential increase in technology we see every day is creating wealth at a ridiculous pace. Our parents did not have iPods, cell phones, e-mail or social networks (facebook, hacker news). Try living without any of these for a day to see how "rich" your parents were at your age; who knows what will be around 20 years from now?

We take these things for granted and don't consider them "making us richer" because they are widely accessible, and people have a tendency to consider themselves rich only when they are richer then their neighbors.