Taking my toothbrush out of the bathroom for the fist time at this point in my life because of "the germs" would be paranoid behaviour, in my opinion. It's not that there aren't germs, it's that they've always been there and I'm still here and healthy.
I also don't understand what your toothbrush has to do with this. Please try considering this from the perspective of establishing practice for a bathroom shared by more than one individual: its probably important to know if closing the lid is an effective hygiene technique or not.
Did you expect my answer to be 'yes'? Genuinely curious about what you're trying to get at.
Your immune system did not evolve to function in a sterile bubble. Some people were traumatized as children to be so afraid of microorganisms that they make ridiculous decisions.
The biggest culprit of foodbourne illness is sick cooks with poor hygiene. Not the failure to bleach every surface in your bathroom every time someone flushes the toilet. Oversterilization is a strong suspect in many sources of disease.
This study suggests ways to prevent those cooks from becoming sick