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.
Just think about all those public restrooms with like 8 toilets in a small area, all of which have no lids (not like anyone would put them down anyway) and use those super high pressure flushing mechanisms!