I agree that it's useless to speculate....however, I'm going to do it.
I tend to be the same way as this lady. In theory, I always want to make new friends, and so I reach out to people. However, when they get too close (merely coming to my church would qualify for me as getting too close, sadly) I get rattled because I'm such an introvert. I pull back in my shell.
I agree that small acts of kindness that don't ask anything of her would be the best approach. She'll warm up.