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You see there are no studies disproving this theory therefore there must be studies disproving this theory, therefore this theory is wrong.That is an oversimplification, and I think it's in the original article. Let me try to give an alternative explanation.
In an ideal world where all the studies have the same amount of subjects and all the countries have the same conditions, when you make an histogram of the result of the test you expect to see a Gaussian distribution. Some graphics in https://en.wikipedia.org/wiki/Normal_distribution
If half of the studies have 100 participants and the other half have 10000 participants, you expect to see the sum of two Gaussian distributions with the same center, it looks like a low wide mountain with a bump in the center. In a more realistic universe, each study has a different number of participants, and you get something in between. A rounded symmetrical bump.
Also, in a magical world where there are two type of countries, you will see the sum of two bumps with different centers. If they were far enough, you would see two humps. If they were too close, you will see only one hump but wider than the expected only form noise. And in between you can get weird shapes.
In a realistic word where each country is unique, and they are not so different, you get a bump. With enough variations, some luck, and crossing your fingers, you expect to see a bump that is similar to a Gaussian. It's not exactly a Gaussian, but somewhat close enough. More technical details in https://en.wikipedia.org/wiki/Central_limit_theorem
So if you have a very big number of studies, you expect to see in the histogram something like a Gaussian. In the first graph, instead of the histogram, the article uses another representation. In an ideal word, you expect to see an inverted ʃ. See again https://en.wikipedia.org/wiki/Normal_distribution
In a real word you expect to see something somewhat similar to an inverted ʃ. But the graphic shows only a L, Where is the top horizontal part of the inverted ʃ???
It's a very difficult question, and it's difficult to understand without a deep analysis. (That I can't do.) Perhaps there are good reasons, but it's strange.
In particular, the vertical part of the inverted ʃ in the graphic is close to 0, too close to 0. You can see that the lower tic of the inverted ʃ goes quite a bit to the right, so the "missing" upper tic should go approximately the same distance to the left. (Or there must be an explanation. Not all distributions are symmetrical, but it's strange that it's so asymmetrical.)
Now, the "missing" experiments in the "missing" upper tic of the inverted ʃ are the ones that say that the hypothesis is wrong (or even that lead is good for you). So it would be nice to have an explanation of thee weird distribution or the disappearance of these experiments.
Oversimplifying, there are no studies disproving this theory, but from the distribution there should be studies disproving this theory, therefore there is something weird happening here.
(Note: Sometimes the vertical part of the inverted ʃ is so far away from 0 that you don't expect any result in the negative part. Just the two tics at the top and at the bottom of the inverted ʃ, both in the positive part.)