Did the app really grant them continuous access to user info? I thought it was a one-off thing - they get your data at the time of use (and your friends') and that's it.

Plus the approach you outlined would require the user to like/dislike things based on the add they saw, so CA can observe a change in the predicted affiliation (they didn't have access to posts as far as I know). I don't think it would have that effect (even if the add influences you, I doubt that it would make you go unlike Obama's page for example). Not to mention that by any likelihood you shouldn't be able to verify that a particular add was shown to a given individual.

I suspect it was a simpler use case - they would group users into segments, and then craft different add strategies for each one (maybe based on other research or just expert opinion).