I don't think their study is wrong, I think they've drawn the wrong conclusions though.
If you're smart, you're more likely to go to university, secure a higher paying job etc. You're likely to marry a spouse of similar intelligence. Your kids will also probably be smart, and go to university, and earn a higher wage, and marry someone smart, and have smart kids, repeat ad infinitum.
It doesn't mean poor people can't be brilliant or rich people can't be thick as the proverbial pigshit. But as a rule, intelligence, in whatever form, is more likely to beget financial success.
The results will be further skewed by the fact that if you're lucky enough to be born into a rich family you'll likely go to a private school or have private tuition, possibly better nutrition, have the security to be able to do countless unpaid internships and volunteer projects in order to secure said high-paying jobs that someone of equal or superior intelligence simply can't afford to work towards.
They've got their cause and effect completely backwards. Wealth can't create intelligence, although it can give infinite advantage, but intelligence can create wealth, assuming it's correctly applied.