They established this in one of the most disturbing MythBusters episodes years ago.
edit: actually, I’ve realized in that episode that the toilet didn’t have a lid, so while the experiment wasn’t the same, you can probably draw the same conclusion when control toothbrushes outside the bathroom were also affected
Still looking for the episode, but here’s a short writeup
https://tvovermind.com/far-worst-thing-ever-discovered-mythbusters/
edit: looks like it was episode 12
https://mythresults.com/episode12
https://mythbusters.fandom.com/wiki/Break_Step_Bridge_(Episode)
edit2: This is it from their Facebook page
https://m.facebook.com/MythBusters/videos/surprise-toothbrush/10152461851823224/