It's possible that it was just a total accident - maybe she was using the "find friends" feature to try and locate someone...it grabs all your email addresses and tries to match those to people on facebook. If she were using that and accidentally checked your name instead of or in addition to the one she wanted, you'd have gotten a friend request.

Once, when I was syncing my phone contacts, facebook tried to add as friends all my contacts, and I had to stop the process real quick, because that's not what I wanted to do. Maybe something similar happened to your T.

Only way you'll know for sure is to ask, but I bet it was a random accident, and she probably wasn't looking at your FB page, or anything intrusive. She probably also didn't decide to invite and then un-friend you because she changed her mind. It was probably more of "oops, that didn't do what I meant to do...now I have to unfriend all these people."