That's seriously absurd. Are the any instances of this being enforced in a public park? I've read of many cases of getting added to the registry from public urination, but they're all in cities[1].
[1]: And usually it's not even in "public". It'd be behind a dumpster or the end of an alley. Yes it's not something we as a society want, but who in their right mind puts that person in the same category as a pedophile.