A message I'd want to send to my own DD is this: People judge you based on the signals you send them. So if you're awake and messaging people at 2am, esp. if you're younger, people may think this tells them something about you. If you're being a little bit flirty with them, they may think it tells them something more.
Be alert to that, and remember it when you're evaluating your communication with other people. And think about the messages you want to send.
I feel like this is way too close to victim-blaming for comfort. It feels similar to comments about how one is dressed, etc.
I'm frequently online at 2am because I battle insomnia and have odd work hours. It says nothing about me at all to be online at that time and I don't care for the implication otherwise.
I think there is a significant difference between adults being awake at that time, and 10 or 12 year old children that still have to go to school in the morning and need their sleep.
And nobody said it was a fantastic idea for her to be awake then, and in fact in my first comment in this thread I mentioned that she'd committed a bedtime infraction (and I also think talking to her about how that impeded her functioning the next day is fair game). My point was that it's wrong to impute sexual connotations to being up late, as in "people will get the wrong idea." I was an insomniac as a teen too, and the most goody-goody teen imaginable. Some people are just insomniacs or night owls, and it doesn't mean they're asking for it.
As for the OP, it sounds like you handled it well, and I'm sure she's glad to have you in her corner.
OP-I agree with everyone, it sounds like you set reasonable boundaries and are also enforcing them in a reasonable manner. Your FB limits were perfectly clear and appropriate, and the violations in use were also clear.
As far as being up at 2am saying something about you-I have had intermittent insomnia my entire life. If the internet had been as ubiquitous when I was a kid as it is now, I probably would have been on it at 2am on a not-infrequent basis. As it was, I spent a lot of middle of the night time watching horrible informercials and even worse movies. I think my mom would have preferred the internet-at least that is quiet and doesn't involve KISS at an amusement park or Alice Cooper with a jar of liquid evil.
If it is a violation in the OPs house to be on the net that late (or even up that late) then it is perfectly reasonable to punish/discuss/whatever is appropriate.
But I do think it is a bad idea to teach kids that "you were putting out signals by being on the internet at 2am" is valid in any way, shape or form. It comes way too close, IMO, to blaming people for doing things that are out of the norm, rather than blaming the creeps who read something into that.
Being up at 2am, even if you are a teenager, doesn't send a message or tell people anything about you (except that you are up late). People might read something into it...but people will also try to read meaning into TV test patterns and the late night activities of kittens.