It it interesting to see the adversarial relationships we set up with our kids displayed here.
Kids just want to be heard and trusted. Taking away stuff never "teaches" them a lesson, it only teaches them how to be innovative in ways to avoid punishment (think back to when you were a kid). It also teaches them how not to tell you things for fear of reprisal.
I see nothing wrong with her having a FB account and you friending her and/or having her login info. Tell her about the dangers and concerns about privacy (I personally think facebook is a terrible invasion of privacy, but I am in the monority these days and it is how kids do things, ain't no stopping it now as they say).
Examine what your real concern is - if it's some bad guy friending her you will be able to see that, or if it's that she's sharing information she shouldn't, just talk to her about why she shouldn't say "3 week bahama vacation starting tomorrow!" She should be able to understand your concerns, even though kids do have an "it won't happen to me" attitude (again, think back, you had it too).
Work together, not at odds with each other, to find a solution you both can live with.