// News of the original paper merely said that MOND had been verified at a 5 sigma level ... //
To a certain extent, anybody should have stopped reading at least the *report* at that point. I won't comment on the merits of the original paper, which have been discussed in depth in the link I provided; but your ***-detector should be in high alert at the point that it's claimed that such a paper is in any sense definitive.
Take the "at 5 sigma level" part, for example. I wouldn't here wish to undermine at all the idea that "5 sigma" is a useful threshold, a gold-standard even, for confirming some given observation. But that comes with a few caveats. First, and perhaps most important, is that in a paper like this it's being attached to a secondary analysis. The author of the study claiming to have verified MOND is not part of the "Gaia EDR3/DR3" team, which is to say that he's analysing somebody else's data set. Analyses like that are evidently not necessarily wrong, but it's a factor to take into consideration: whenever you are using somebody else's data set, you might be less familiar with how it was generated, what its limitations may be, what assumptions went into evaluating the given uncertainties, etc. You'd hope that all this would be made available alongside the data set, and indeed often it is, but even still there's always that barrier between the "author" and the "reader" that can play a role.
In a case like this, it's even more relevant. Without wishing to accuse the author of definitely publishing results that happen to favour their pet theory, what is at least true is that somebody who hadn't come across the "AQUAL" variation of MOND is rather less likely to have written such a paper with such a bold conclusion. As an example I'm more familiar with, I mentioned muon anomalies. The one that appeared in the media recently is about the "g-2" anomaly, but there have been a few others all linked to muons from the last decade or so. If you want to look them up, search for "RK anomaly" and "P5 prime anomaly", or have a look at the (now slightly out-of-date) review in
https://arxiv.org/pdf/2110.13270 . The technical details don't particularly matter, but what *does* matter is this: firstly, the anomalies seem to be disappearing one-by-one as more data are gathered and as theoretical analysis improves; secondly, at least individually the anomalies were never at 5 sigma level, and it's only secondary analysis (eg Alguero et al
http://arxiv.org/abs/2104.08921 , claiming up to a 7.4 sigma deviation(!)) that suggested otherwise; thirdly, even if after all they remain, some of the wilder interpretations touched on in that review aren't necessarily responsible, and a more plausible interpretation is that we're messing up the predictions somehow, by missing or miscalculating something that we are already "able" to account for within the current theory. London/Matias seemed to downplay this explanation, and it's interesting to me to see them argue that even a recent experimental result ("note added" at the end of the review), leading one of the anomalies to almost disappear, end up "reinforc[ing]" the case for the new physics that Matias has spent much of his recent career looking for. (NB I know Matias, he's a good physicist, and in his defence once told me that he spent his entire career "hoping to be wrong", because that's the more interesting outcome. A good attitude to have, in other words; but "reinforc[ing]" is a subjective term here that I cannot agree with).
TBC