Just because your communication happened on paper doesn't mean that they haven't stored your email address or phone number in some service digitally, and that somehow that info has been shared (e.g. a phone with a facebook app that uploads all contacts)

I brought it up to her, we wondered how it happened, and she admitted that she'd searched for my profile a week before.

I'd say this aspect of the system is a good feature. If you're searching for someone, it's nice to give them an opportunity to "independently" reach out to you.