OH YES YOU POSTED THIS
I'm sort of leaning towards the dad's side of the argument, but less so then I was when I first watched the video. I've grown up in a really spoiled lifestyle. (No chores unless I feel like earning money, my parents do most things for me and usually buy me what I want or help me find ways to earn them, they find jobs for me to apply to, help me with applications, ECT. But then in return I think I'm pretty nice to them. I work hard in all the things I do have to do and I'm nice to them.) So I can't really relate to the girl and how she would feel. I'm Facebook friends with my mom so I wouldn't post anything about them there. If I wasn't I probably still wouldn't post anything about them, because even with blocking them there's other adults I'm friends with who could see it. Without them still doubt I would do this type of thing just because Facebook doesn't seem secret enough. I might post something about them here or on tumblr (if I ever figure out text posts xD ) If they found those I'd probably be grounded and have my computer taken away for a long time. It wouldn't be shot at because my dad doesn't own a gun, but it's pretty practical for them to take it away forever if I'm swearing at them and stuff. (swearing isn't allowed in our house and I never do) I'd be really upset but on their side it probably seems fair. Not doing things is one thing but being disrespectful is a lot more upsetting to adults and people in general.
I'm sure the daughter felt like things weren't fair, and it seems like her parents are pretty strict. It's probably hard to deal with, but at the same time when you've been brought up strictly your whole life it seems like it would become sort of a habit-thing to do chores and things, so it wouldn't seem like you were a slave, just helping to your family. If she doesn't get that everyone has to contribute and it'll be fair that way maybe her parents skipped an important lesson when she was younger. That would be their fault, but it still seems like she should've adjusted.
I wish I could stalk their family and know everything so I could understand it and be fully confident in my judgment. If the dad made it clear that she wasn't the cleaning lady and how important it was due to respect I could see him getting upset. But the girl might've just found it easier to call her the cleaning lady and not bother explaing the situation. We have a cleaning lady, but my mom doesn't let her clean my room unless I already have it somewhat cleaned up. I used to not get why, but my mom explained that I need to have some responsibility too and we need to be respectful and not give her a crazy amount of work or anything. It's sort of weird to me since she works for us, but it makes sense. If he didn't explain then it's their fault.
In theory I agree with the dad, but I'm not really sure. It's hard to make judgments on how families work without being there or knowing everything about the situation.
The girl probably should've found a different way to vent if she needed to do this. (as a bunch of others have said)