Cochrane meta studies are the gold standard. In general they do get taken as proof.
As a matter of simple Bayseianism, P(result is correct|result is unusual) depends on the frequency at which conventional wisdom is wrong, compared to the frequency at which other things (errors and statistical anomalies) exist that produce unusual results. The probability that the result of a study (or meta-study) is correct given that it produces an unusual result is not equivalent to the overall probability that studies from that source are correct, so "Cochrane meta studies are the gold standard" is not the controlling factor. (Imagine that 0.2% of their studies are erroneous, but conventional wisdom is wrong only 0.1% of the time. Then the probability that a study is right given that it produces a result contrary to conventional wisdom is only 1/3, even though the probability that studies in general are right is 99.8%.)
That's why we have maxims like "extraordinary claims require extraordinary evidence".
FYI it isn't even clear the review he mentions says what he thinks it says, not to mention the reviewers noted most of the studies had high risk of bias. "Other therapies" as controls in the studies doesn't necessarily mean therapies that are considered to be effective.
I just finished the first draft of my essay, "Are Sunk Costs Fallacies?"; there is still material I need to go through, but the bulk of the material is now there. The formatting is too gnarly to post here, so I ask everyone's forgiveness in clicking through.
To summarize:
(If any of that seems unlikely or absurd to you, click through. I've worked very hard to provide multiple citations where possible, and fulltext for practically everything.)
I started this a while ago; but Luke/SIAI paid for much of the work, and that motivation plus academic library access made this essay more comprehensive than it would have been and finished months in advance.