My mom actually taught me "Never wash your hands after peeing in a public restroom, because the faucet handles are dirtier than your body."
And she's a doctor.
I think the advice is as much about the chance that you inadvertantly touch the toilet as your own urine. Afterall, urine being sterile means your hands are probably dirtier going into the process than coming out, at least with regards to bacteria.
I was just wondering. Human minds are messed up in 1001 ways, but are there a few rational principles that most people already have down? Of course, the answers to this question are probably so extremely obvious that I haven't even considered them. But I ask all the same.