I agree on both fronts actually. They could very easily be having an enjoyable but innocent time together. My fiance and I have slept in the same bed together without touching each other inappropriately etc. We even know an engaged couple who live together and sleep together in the same bed, yet they have never had sex etc and are deeply religious, or so they tell us! Also closing the door simply means that they would like to spend time with just each other, because for my fiance and I, that is the time that we can talk about serious and very personal stuff, and be affectionate with each other in private. And for most people, displaying affection is an especially private thing.
However, they could just as well be doing or thinking inappropriately. I would certainly agree that sometimes, lying down together poses some temptations and my fiance and I have been guilty to giving in to these temptations to some extent. So we’ve given ourselves rules and made strategies so that even if we are lying down together or are in a bedroom together, we don’t fall into temptation.
Therefore, it is all about the couple themselves, their personal beliefs in adhering to the catholic faith. It may be a good idea if you and your flatmate are close, to casually bring up the subject, but be careful that he doesn’t think you are prying into his personal life. Good luck! and good on you for thinking of his spiritual health.