I voted yes, but with conditions. Did I trust the young man? How far away were they going? Where were they going? I would actually be much more concerned with personal safety i.e. two teens driving a long/unfamiliar distance by themselves or staying somewhere unfamiliar or possibly unsafe than I would be with sexual issues. IMHO they can DO IT just as easily in the backseat of a car as they can in a hotel room. And
reputation is the farthest thing from my mind. Egad, whatever, get over it. If my teen isn't worried, then its none of my business.
Funny story though. When I was 17, the summer before my senior year, I was checking out colleges. There was one I really wanted to see, and the only time I could go and get appointments to meet with everyone I needed to meet with, my mom absolutely could not get away from work to take me. At the time I was dating my music accompaniest (I was a flutist, he played piano for me in competitions) - that in itself is a whole twisted story, suffice it to say not one of my better decisions - he was 4 years older than me. A fantastic musician, brilliant future, etc etc, except for the fact that he was 21 dating a 17 year old.

Mom wasn't crazy about him, but he was in all other ways quite responsible, so she kept quiet and just watched. Yes, we were having sex, yes it was safe sex, yes I was on the pill, yes, mom was aware of this.
Anyhow, he offered to drive me to this college to check it out - 600 miles away. Required a weekend trip away, 2 nights in a hotel, he offered to drive, and pay. No way would she let him pay, but after much discussion, we took him up on the offer to let him drive. The weekend was fairly uneventful, we had an OK time, the college was very nice, and it was fun, at the beginning, to play "married couple".
Let me tell you though, nothing like being with someone 24/7 for an entire weekend to let you know exactly how you feel about them. By the time we got home he was driving me in-freaking-sane, and I am sure I was doing the same to him. He dropped me off, helped me unload my stuff, kissed me good-bye, and drove away and I said to mom "OMG get him away from meeeee!!! I can't stand the sound of his annoying voice one more second!!". Mom just smiled.
We broke up a week later. I had to find a new pianist. That part sucked.