The parent is not saying the author made an incorrect claim. They are saying that the parent did not continue their argument to arrive at a conclusion that someone else had, the conclusion that causal models are what tells you when you can combine datasets and when you can't.
Your job when analysing data is simply to enumerate the possibilities and assign likelihoods to them if possible. If two models fit equally well, you're supposed to write them both down in the hope that someone will collect further data to distinguish between them.
If you're cutting holes in your report for political reasons, that's just not doing the job. That's what pundits are paid to do, not (ideally at least) scientists. Fraud is easy to commit, and the fact that it's possible is not that hard of a philosophical issue.
How do you tell that a paper containing conclusions to support an agenda is written with correct scientific rigor, rather than fraud? Using Simpson's paradox, one can obfuscate their biases by making the desired conclusion drop out of the data.
Simpson's paradox is about a data conflict between an overall view and a more specific view. For example, in the kidney stone scenario, say you find treatment A is more successful overall and treatment B is more successful in the specific view at both treating small stones and treating big stones when broken down that way. The article indicates that the specific view is always correct so treatment B should be used in the future, whereas the commenter is saying that context is important to determine which treatment should be used.