Although Mythbusters is not a peer reviewed scientific source, they do employ reasonable standards of experimentation.
And the first source you posted is particularly interesting, with similar conclusions to what I remember from Mythbusters; that lids reduce the total number of particles found, but that the particles produced from lid use last longer and are larger. So a lid closed situation can;t really be said to be more hygienic.
Unfortunately on a cursory skimming of the other articles none of them seem compare toilets with lid down to lid up, they all seem to look at lidless toilets only. Thus, they can;t really speak to the topic of lid use being more hygienic without the direct comparison.
Yes, I followed the ones posted. None of them say the opposite, they all leave out the results from the lidded flushes. And someone else posted a paper that showed that although lid closed produced fewer particles, they were larger, and lasted longer, so flushing lid closed was not particularly more hygienic.
toilet humour (lemmy.world)