The point is we do not have the data. We 'only' have Inmarsat's interpretation of the data.
"We" don't have much choice in that regard, since it's "their" system that has yielded the results, and "they" know more about how it works than anyone else.
If they say too much about how their system works, then they might be more prone to interference or jamming.
If they were to publish their analysis as a novel technical result or a patent, then the journal or patent office would send it to suitable experts to review.
If they were to submit it to a preprint server, then everyone qualified could have at it, but the best arbiter of the quality of this analysis would remain Inmarsat's own professional pride and responsibility.
The chance of a random blogger finding a crucial flaw in Inmarsat's timing and/or frequency shift analysis is not great.
The Lost Ark would have been investigated by "Top Men", who would include Jones' peers - and rivals - and who would be well known to Jones, if the general had been the boss of a patent office or a journal editor. It would be normal for their identities to be kept from Jones, to avoid the suggestion of any collusion or potential unfair influence.
However, if anti-Inmarsat noise builds further, then the company probably will have to release their arc/speed results. It won't quieten any hard-line conspiracy theorists, but it would allow any reasonable commentator to be absolutely certain that the missing 777 went south.