>It is possible, but not to the degree that all long Covid cases are being confused with external factors.

Didn't mean to imply that all cases are, just that our definition of and knowledge about long COVID is nebulous enough that some nontrivial proportion of cases are likely attributable to external factors.

>Additionally, long Covid can cause brain fog. This was shown in brain scans from a popular HN post about a research paper just yesterday

Absolutely, just as other infections can cause severe lingering symptoms [0]. But we don't really know how prevalent these are, nor the severity of the prevalence. Studies like the one you link typically select for the most severe cases. We don't know whether it's useful to generalize from those.

[0] https://en.wikipedia.org/wiki/Post-acute_infection_syndrome

You can't see "brain fog" on any imaging scan. That study didn't demonstrate any such causation. At most you can establish a correlation between certain imaging patterns and patient symptoms (which are notoriously noisy for any sort of behavioral health condition).