This phenomenon – of using data analytic methods to "prove" a contentious political issue one way or another – is more often found on the Left. But let's not forget badger culling, where "the science", if anything, was found to detract from the "Culling badgers will alleviate bovine TB" hypothesis. I've written about that (endlessly), here and here, yet the cull continues, under a Right-wing administration. Sometimes the politics trumps the science.
And that is entirely the way it should be. Bayesian statisticians can explain what's happening. The commonplace view of scientific method is that hypotheses ("Inequality will always rise", "Inequality causes depression", "Temperatures have just shot up", "Culling badgers cures bovine TB") can only be rejected, or falsified. Experimental data is used in an attempt to "disprove" the null version of these hypotheses (that is, their converses: "Inequality isn't rising", and so on), in a fairly antiquated and hugely flawed statistical process known as "significance testing". If a significance test is positive, people not trained in statistical reasoning – newspaper columnists, Leftists with books to sell – have a tendency to start claiming that "the science has been proven."
Über-litigant, Michael Mann, saw his fraudulent 'Hockey Stick' crumble along with his bogus claim of being a 'Nobel Laureate.' See his incredible shrinking résumé and accolades on his Penn State bio. Before. After.
It hasn't (even those statisticians who continue to hawk significance testing as a valid approach to induction wouldn't make that claim), and in any case, this isn't how our reasoning about the universe works. We come to any particular policy topic with a set of preconceived opinions. New data will modulate those opinions, in a process which can be explained by Bayes theorem. If new data is hugely strong, in terms of the signal it contains about a hypothesis, then people whose opinions are very different a priori will, a posteriori (literally "after the data are seen"), converge in belief. If the signal in the data isn't strong, they won't.
That doesn't make either side of a political argument irrational, merely that data of insufficient strength has yet to be generated to overcome the (perfectly) valid world views of different human beings. You can intuit what I mean through a thought experiment. As a Tory, I have hugely strong belief in the importance of the integrated family unit with regard to positive outcomes for children. It would take more than a single study in a sociology paper which "proved" that there are no "significant" detrimental outcomes to children raised in "alternative" set-ups, to cause me to discard my theory. But if you are a liberal, with a strong belief in the alternative ("Family set-up doesn't matter"), then a single study may well have quite a strong impact on your belief. You would end up on Radio 4, claiming "the science has been proven".
The political mess is caused by two separate things, neither easy to fix. First, our culture has decided that science is "objective", that the probability of different theories being true is somehow utterly independent of the views of the men and women who decide which theories to investigate, or the manner by which those investigations proceed. I reject (ironically!) this idea that science is objectively objective, which makes me a Bayesian. We remain in the minority but our views are gaining ground.
Secondly, and less philosophically, we have a problem that there simply aren't enough journalists and media commentators properly trained in the quantitative discipline of statistics in order to subject claims such as Piketty's to rigorous analysis. As a statistician who also plies his trade as a political writer, I would say that, wouldn't I? Maybe I should read fewer novels, and pick up more economic textbooks, after all.