What would you do? How should I respond to this?

Dr. Shane,

My 15 year-old daughter and I have been arguing for the past month. She has a new boyfriend and wants 'alone time' with him in her bedroom. I've told her there is NO way that is happening. She throws the 'trust' thing in my face and I tell her that it isn't about that. Am I being too 'old school' on this? Should I trust her and her boyfriend with the door closed? What would you do?

Thank so much,
Laura