This is not government obviously, it's private sector.
It's simple...what I do outside of work should not be up for scrutiny unless what I'm doing is illegal or puts the company in a negative light. Example...if I go to a casino and do my thing...shouldn't be an issue. It would be an issue if I am on a work-related business trip, stop in a casino, and get into a fight and arrested. I don't have FB or Twitter, partly because I'd have situation where I'd deal with a lot of people I don't know and don't care to know.
Is this a hill to die on? If need be, yes. My company has no regulations in regards to FB or Twitter usage outside the workplace. She's 22 and not necessarily the most mature, but she does a good job for me and her personal life doesn't affect her job. I can live with being called boring because I don't go out and party with them. This VP is being a jerkwad about the whole thing and he is abusing his power. I will not be bullied or intimidated, period.
That's the key. Should.
Should is not what it is in reality.
"Should" is what Cat posted. However, that is not reality. The reality is that if you post something incriminating about a co-worker/boss/workplace in a public forum, you're gonna get in trouble.
What kind of consequence was he looking to instill? Termination? Verbal warning? Suspension? As I wrote earlier, if there is something about harassment/disparaging a co-worker in a contract or policy then he could easily fire her because calling him creepy and whatever else would fit under that. He has more than enough cause to let her go (and if you guys have no contracts, in the eyes of the law he is still justified. If it is an at-will employment kind of deal, he wouldn't even have to use the "she called the VP a creep" out, he could fire her just for the fuck of it).
If it was going to be a verbal warning, I would have just done it. Now it sounds like you have escalated the situation and there is the potential that it could cost both of you your jobs (which may be fine for you, but does she have 3 options she could go to at the drop of a hat?).
If it was termination or you could tell he was leaning that way, then disregard the above and fight what you think is worth fighting for.