Given the Gray Lady's current set of leftish biases, you can imagine DeParle worked hard to find evidence of social immobility in the U.S. vis-a-vis Europe and the other English-speaking countries. By focusing on the very top and very bottom he found what he wanted.
DeParle did admit that in the great middle, the U.S. is still mobile. He writes:
Middle America remains fluid. About 36 percent of Americans raised in the middle fifth move up as adults, while 23 percent stay on the same rung and 41 percent move down, according to Pew research. The “stickiness” appears at the top and bottom, as affluent families transmit their advantages and poor families stay trapped.Most of us are neither in the top nor bottom tenth of the income distribution; economic mobility remains a reality for us - no surprise. You have to get to the second page of the article to find this quote, that's the Times' liberal bias at work. If you read all the way to the end, it is a decent article worth your time.