I didn't believe "ugly crying" is about negativity. Rather, the "ugly" bit is about the abandonment with which one cries. One is so invested in the emotions (whatever those may be--it's not even a continuum of good/bad but rather a huge, high dimension vector space) that one abandons propriety and self-respect and just cries. It's about investment due to the exceedingly high emotional resonance with the subject matter.

This is my understanding. Caveat: I am not a person who cries much, if at all.