Mythbusters found it makes virtually no difference, and lid down can actually make particles go further due to the pressure forcing them through a smaller gap.
They also, for some reason, last about 11minutes longer in the air when closed. The studies are misleading because they say there are fewer visible particles, but the bacteria count remains the same.
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.
I'm not sure how this qualifies as being any better, I read this one previously and found it to be lacking in actual data information. It makes claims but literally anyone can write whatever they want on the Internet. It's not enough data and not clear on how they actually measured or how many measurements they took
Myth Busters are not a solid scientific source. I discussed the issue a bit, linking to some papers in another comment here:
https://feddit.de/comment/5298414
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.