Peeing in a park where there could has been children can put you on the list, with the rationale being that while urinating in public you're also potentially exposing yourself to children. It's definitely outrageous that it's on the same scale, but it's not like peeing on a dark alleyway at 3 am will do it.
I did some light research about the subject after I stopped laughing and crying.
It seems like it depends on the state, there are 13 states that have the "public urination leads to sex offense" regulation. Of those only 2 states have the "near a minor" clause. So 11 states can put you there for peeing in public, no strings attached. On those, you would be at the mercy of the police officers that catch you.
Also, I found out that the reason for the "public urination is a sex offense" is not urolagnia (at least it's not overt urolagnia), but a means to deter the flashers' defense "I was peeing, officer." Not sure it makes a lot of sense.
Disclaimer: As I said, this was light research on the topic, so there might be errors. Sources were mostly Straightdope forums and the Wikipedia, IIRC.
I tend to agree with getting put on some kind of shame list if you get caught urinating in public though. If you're regularly getting caught pissing in bushes you are obviously really bad at not having people see you pissing in bushes.
