"I am not her friend, I am her parent."
Couldn't have said it better myself. I'm not sure what kind of responses you've gotten here on this, but I can imagine that some of them were probably ridiculous. There's not a question you can ask on this site without at least of couple of totally outrageous responses.
Case in point, I just asked a question about a scorpion infestation in my house (we have the extremely dangerous type here in AZ) and a couple of women actually felt sorry for the little demons and suggested I "learn to live with them." You just have to laugh at stuff like that because you KNOW that if these folks were really in our shoes, they would feel much differently.
As for your daughter, I think you handled it exactly how I would have. I just glanced down and saw another person told you never to "threaten" your child. Again, I just had to laugh. I probably threaten my kids a dozen times a day, lol. Honestly, you did what you had to do to make her understand that you won't take a threat from HER lightly. You completely disarmed her and put the control back where it belongs...with you.
Sounds like you're doing a great job with her, especially since the two of you are so close. I can only hope when my daughter is that age, I'll have that kind of amazing relationship with her.
Wishing the very best for you and yours.