Doing anything by way of an experiment once is slim proof, something that applies to both papers.. And since Davies negative replication came after NASA's positive he would logically be required to theorise about reasons for false positives. I have no doubt that the large and very experienced NASA crew also though a lot about potential false positives, and could if required written a half-dozen papers on the possible causes for these. But since they were 'head over the parapet' first they probably saw little reason to expend ink on explaining something which as far as they were jointly concerned was not the case. If they had as much doubt as you have, Tom, they would never have published.
So I agree with the first sentence here - which would be the case for not publishing the unusual result. If all you have is slim proof, then something never before noted and unexpected is likely an anomaly. But that is a recipe for never publishing anything unusual. Properly, the caveats that make the results weak could be mentioned.
Otherwise... You seem to think that publishing of experimental results should be somehow conditioned on belief. I think the reverse. Experimenters should (many do) do their best to make results transparent and strong. Where there are known potential issues they should explicitly acknowledge them. For example, in this case, since radon progeny is a well known issue here (I guessed it myself in print here for one of the amateur false positives, and it turned out to be confirmed as that) , I'd expect them to comment and note the methodology they used and whether that made differential radon progeny pickup likely. If they had done that their results would be stronger, and whether the result is replicated or not their credibility publishing would be better. I see no reason not to do this, and every reason to do it.
Equally, now, if they are confident there remains a mystery and their results are sound they could do two things. (1) disclose the methodology that allows them that confidence. (2) repeat the experiment and obtain another positive with better checks. Just as Davies did, when he thought there might be a problem in his first replication. For such an important result - of real interest to many people - anyone would go the extra mile if they could.
Why you expect them to remain silent in that case I do not understand.
