No, I don't think it's about trust. Rather, it's about not allowing them into certain situations yet.
To give an analogy, I feel fairly certain my daughter isn't going to drink in high school. Regardless, I wouldn't knowingly allow her to go to a party that I knew was going to revolve around drinking. Even though I trust that she has made her own personal decision about that, I wouldn't put her into a situation where serious temptation would come into play, and a situation in which she could get into trouble for what other people are doing.
It's not about trust, just as it's not completely about sex. I don't say yes to everything my daughters want, even if it's something that's within my power to give them. And this just isn't something that's right during high school. Well, yes and no. You're right to say that no one's going to come around and do a bedcheck. But dorms do offer certain protections that private apartments don't. In my old dorm, a security guard was on duty after dinner, and only residents /their signed-in guests could get into the building. Perhaps more importantly, so many people lived in the dorm that IF a girl found herself in a compromised position (perhaps having allowed a guy into her room, and then regretting it) she could've yelled, and someone in the next room or in the hallway would've heard her. And there was also a code in the dorms: If a girl'd let a guy in, and she wanted him to leave but he wouldn't . . . she'd pretend to go to the bathroom, and she'd ask another girl to drop by her room a moment later to make herself annoying. The other girl'd just camp out in the room, turn on the TV, ask for help with math, make herself at home until the guy finally decided he'd have to leave because nothing fun was going to happen in that room that night. As an RA, I was frequently asked to be the annoying person!
So "supervised" might not really be the right word, but I do think a dorm's a little safer for a girl who's living away from home for the first time. Even so, I was aware of a number of rapes that occured in our dorm -- always date rape type of situations.
Horrible story: I remember a girl whom I knew just in passing in the dorms; she moved into an apartment because she wanted more freedom. A man threw a brick threw her sliding glass door, raped and murdered her. It was her first month in the apartment. Also, that story is very off-topic.