I think in public internet forums that people are loathe to attack someone in public. As one of the previous posters mentioned, what is on the internet can be seen by anyone. I think it respectful that if someone disagreed with your opinion, that they did not attack you out int he middle of the forum.
I equate it with this: would you rather get in a fight with a SO in the middle of a crowded restaurant, or would you prefer it to happen in private?
If you don't feel comfortable with her response to you via PM, talk to HER and not the forum about it.
Some people call it 'not airing their dirty laundry'

I don't know what was contained in the PM nor do I care, I'm just saying my opinion on this as a member of various forums where things like this have happened. I, for one, think it good that someone who disagreed with you addressed it to you only, and did not clog the forum with vitriol.
K.