This seems like something that should be true, but I think I remember seeing a Mythbusters episode where they decided it didn’t make a difference. That show was more about entertainment than science, so I wondered if there was a more rigorous study done? I’ve definitely seen splashes of water(?) come out from flushes so that alone seems to argue for closing lids.
Ah the ol “it’s not 100% effective and guaranteed to work so you should actually do nothing about it” argument…a true classic in any situation
Seriously though…I never even considered all the splashing and I’m a grown ass adult :/ happily my and my daughters toothbrush live in the kitchen