In 2004, Donald Rubin opined
We do not think that their analyses are estimating causal quantities, except under extreme and unrealistic assumptions.
Now I am not familiar with the actual research, but I am likely to take Donald Rubin seriously. Not only is he one of the founders of causal inference, multiple imputation, and propensity scores, but he has a long history of tackling extremely difficult epidemiological problems. For a humbling experience (for those of us in biomedicine) his CV is here.
I dislike appeals to authority, in general, but claims that researchers skeptical about the value of these testing methods are misinformed seem to be poorly grounded. I don’t want to say Rubin is right about everything but I do think we should take his concerns seriously.
[as a side note, he was also the PhD supervisor of Andrew Gelman, whose blog is worth following]