While I agree mostly with your view, I just spent quite a bit of time looking over the local sex offender lists of several cities I've lived in, and I can say for sure that at least in these random samples, the outliers you mention (public urination, high school sweethearts separated by too many years, etc) are nowhere to be found on any of the lists I have looked through.

I think it's strangely primitive and archaic for this sort of public humiliation to exist in our modern society either way, but a few moments of clicking around these samples at random goes to show that a vast, vast majority of these people have been convicted of what most would consider "serious" sex crimes.