I guess what I find a little strange about her response is how big of a deal is an online friendship? Aren't online relationships used to help one get to know someone else? So that when interacting in real life it had helped you to get to know the person better?

The fact that she seems willing to associate with me in person at the different events, but not online I find really strange. I have contacted people I barely knew from school, and befriended them online, people from work, people from my anime club, sometimes friends of friends just because I thought I might know them or like to get to know them.

Would it make sense that the real reason she didn't want to friend me online, is not so much because of online friends, but maybe her family "checks-up" on her friends on the list or something, not saying they log on as her, but the way the social networking sites are now adays, you can look up the friends of your friends, and so on.