Well dang. Reading this article does provide a couple more details though:

• Another referenced study DID find that closing the lid reduced contamination
• It depends on the toilet shape
• Closing the lid does change the areas that get contaminated in the room (less upward plumage):

So it’s not that simple. All in all (including my other point that most trips require seat down anyway) and as a matter of personal preference (I think its nicer to have the lid closed), I’ll continue to close my lid.