The researchers committed the logical fallacy known as cum hoc ergo propter hoc--in English, mistaking correlation for causation. "They argued," Rosenberg reports, "that the disparities in word usage correlated so closely with academic success that kids born to families on welfare do worse than professional-class children entirely because their parents talk to them less."
In fact, all they did was show a correlation among three observed variables: parental loquaciousness at age 3, IQ at age 9, and school performance in the intervening years. They simply assumed the variable that interested them was the causal factor and that it could be engineered, like turning a dial on a machine, to produce smarter and more accomplished children: "In other words," as Rosenberg puts it, "if everyone talked to their young children the same amount, there would be no racial or socioeconomic gap at all."
Sadly, they forgot to test for parental IQ: maybe that actually drove the whole experiment. Causal tests are more complex than they bothered with.