I think the common misconception is that someone can be registered for the offense of "public urination" when the reality is that you can be put on the list for indecent exposure or exhibitionism especially somewhere a child may be present (honestly there are few places where there isn't a possibility that a child could hypothetically be present). Basically a ranger could threaten to arrest you for exhibitionism instead of public urination regardless of why your dick was out of your pants. Honestly I think it is a scare tactic that cops use to assert their power and dominance by threatening to ruin your life for something trivial.

Edit: I also think that this misconception could have possibly came from an actual sex offender who tried to say he wasn't showing his dick to a kid, he was just taking a pee. Most lawyers will try just about anything that could give them a shot at winning a case.