My parents had exactly the same rule for several months (about 6) into my relationship. They are reasonable and not conservative people either!
Similarly, it didn't make sense for it to be about sex, because we literally were doing that during the day and everybody knew it. In fact, we really only wanted to sleep in the same bed for the perk of cuddling, as we were having as much sex as we wanted anyway!
It was difficult to have a rational discussion about it, because they were quite embarrassed and frankly I felt guilty disagreeing with them (I am a goody two shoes and generally agree with my parents/ get along well).
Eventually when I went to uni my parents just announced that my bf could sleep in my bed.
It materialised that they wanted to keep up appearances to impress my boyfriend's parents! Lol. They didn't want to be the "slaggy" parents. My mum (the more communicative of the two) told me that if I had just invited the boyfriend into my bed at night they wouldn't have had much of a problem. But my dad felt awkward about actually giving the go ahead / they wanted to show respect to my boyfriend's parents.
But when I went to uni, as it was out in the open we would share a bed at night, that made it okay for them to allow it?!
Basically this all happened because of the old fashioned view that sleeping over = sex (when in fact they're basically separate), and the weird tradition of it being "improper" for sleeping over to happen, even if having sex during the day is perfectly allowed! And being too awkward to talk about sex, but just dancing around it by pretending it = sleeping over. Weird.
What's really funny is my boyfriend's parents had the exact same rule in place, for the exact same reason (to impress my parents!) and as soon as he slept in my bed at home, I immediately slept in his bed in his house.
Parents.