You know, I was kinda in agreement with you until you said this. Please read the paper (which had absolutely no information about the Covid stuff in the docs or signup forms.)
Like, one could argue that the major selection factor was whether or not the subject watched TV, which would be fair but not germane to this particular argument.
In fact, the Covid stuff was added after the study had started, and they did a follow-up survey in December 2020 and of the people who reported later Covid, they were indistinguishable from the overall population.
Like, I agree that this would have been much much better if they'd had access to the NHS data and could have joined with the cognitive test data and I personally am not convinced of their modelling approaches, but there's a tradeoff between enough data to estimate important effects, and the accuracy of said data, especially when it comes to medical conditions.
Is your argument that people would preferentially report Covid-19 and throw the intelligence test? Or something else?
Like, this paper has a bunch of problems, but the main effect is not that surprising. The real question is how generalisable the findings are to other viral infections. That's something that hopefully will get investigated more over time.