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.