Btw, I asked the question, but forgot to mention a personal experience of what is a scene in public although it involved no slaps or yellings or anything of the kind. The girl who wanted to try her luck with the 40 year old businessman and is now back calling me on my phone, sometime around December, we were out in the "festive village" that was created in the center of the city, were meeting up for a chat and some hot drinks in a cold winter night.
I was in the mood, came there quite happy, told her two short stories about two stupid girls I had shortly talked to that day LOL and in this moment, she gets...way too dramatic. She accuses me of talking to other girls and all that, I wondered just a bit since there had been more than 1 month she was alright, doing no fights and no drama, but this time it was serious. She started crying and would not stop. People started turning their heads and I was feeling really in a bad spot. She continued crying and I had to "force" her to get up so we could leave. We left, she did not stop crying, I didn't even understand why fully LOL she went on with that, we went on and had a drink a bit later, she calmed a bit down and then she went home.
Have never before that or after that been anywhere near a similar situation, but I guess if it were to happen, it would be best to just walk away. Now that I think about it, maybe I should have walked away even in the above described situation.