Well, according to the Mythbusters, your toothbrush is in danger no matter where you keep it.
Every time you flush a toilet, it releases an aerosol spray of tiny
tainted water droplets. [...] At the end of the month-long trial, they
sent their toothbrush collection to a microbiologist for bacterial
testing. Astonishingly, all the toothbrushes were speckled with
microscopic fecal matter, including the [control toothbrushes] that
had never seen the inside of a bathroom. The confirmed myth
unfortunately proved that there's indeed fecal matter on toothbrushes
— and also everywhere else.
I don't know anyone who drops a deuce while standing up, so even if you were to sit down to relieve yourself, your toothbrush is in danger.