My suspicions have been confirmed. When I studied cognitive neuroscience and when I read news in this area, it was and is very disconcerting to see how often far fetched conclusions about causation are made there on a shaky basis of a small sample size, a multitude of uncontrolled parameters, and correlations only. This new study confirms that more often than not these results are unreliable and unreproducible. A new research paradigm is needed to move this science from stagnation.

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The researchers found that brain-behavior correlations identified using a sample size of 25—the median sample size in published papers—usually failed to replicate in a separate sample. As the sample size grew into the thousands, correlations became more likely to be reproduced. 

Brain studies show thousands of participants are needed for accurate results | University of Minnesota (umn.edu)

I think statisticians have known this for a relatively long time.

Yes, my professor in biological statistics was very explicit about these studies.

Here is a recent example of a study with far fetched, unwarranted, and completely speculative conclusions:

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To study this, Rutishauser and his colleagues worked with 20 patients who were undergoing intracranial recording of brain activity to guide surgery for treatment of their drug-resistant epilepsy.

Researchers uncover how the human brain separates, stores, and retrieves memories | National Institutes of Health (NIH)

Especially with high-dimensional data (incl. MRIs) associations are often spurious. At the same time, only allowing high-participation studies to exist would effectively eliminate smaller labs and result in loss of creativity as studies would only be conducted by a few (successful) folks.

A "darker" possibility is that MRI scans just don't represent well the underlying factors in the brain that affect behaviors. IOW, MRI scans might be a wrong measure, like scull shapes in phrenology.

Regarding sample numbers, aluminium has been linked to Alzheimers but I'm not sure if all victims have aluminium flecks in their brains or just a few.

But on the assumption that there's no smoke without fire, I decided to play it safe and switched from aluminium pots and pans long ago-