f you flush with the lid up, a polluted plume of bacteria and water vapour erupts out of the flushing toilet bowl. The polluted water particles float for a few hours around your bathroom before they all land. Some of them will land on your tooth brush.
I'm sorry, but I think if this was a real problem, most people would be sick all the time. I have known many immacualate housekeepers who did not insist people close the lid before flushing. 99.5% of the homes I have visited through out my life had bathrooms with open lids. Even the homes with those fancy seat and tank cover sets, you know, the ones with matching bath mat and toilet hugger rug, they kept the lids up. Personally, I always thought those lid covers were nasty anyway: just something else for the boys to pee on. My very posh, very immaculately clean grandmother never kept the lids down in her house.
And on the subject of lid-down-while-you-flush paranoia, ever notice that hospitals and doctors offices have no lids on their public toilets? That should tell you something about their concern about polluted plumes of bacteria and water. Obviously the risk is not big enough to be concerned. Probably the auther of the above article is one of those people that uses a tissue to cover door knobs and washes his/her hands 300 times a day.