Sounds like electronic contact devices are your friends.
That way you could maintain a strictly-platonic, not-in-person relationship.
Suppose I might be worried a tad by the question, Why the push by her to be friends? You mentioned that "slight familiarity" is probably all you'd get out of the deal. What would she get, or -- what would she be hoping to get?
I guess if you take up on her offer, do it electronically and "sleep with one eye open." Hopefully I'm being paranoid for nothing, but I've encountered enough fibbing (all sizes) in my day to be ever suspicious. Right now you need more info about what's currently making her tick.