If it were obvious, I wouldn't being doing my job right.
But yes, you are missing something, or I would be cheating. It is not my intention to make this an impossible game. I'm not holding back the difficulty, but I would still like to see someone solve it.
Good luck!
Here's a quick summary of why you have apparently made it impossible. Prod me in the right direction to my logic flaw, or I'll start following up.
The crux of the impossibility is, there are no traces of anyone ever leaving, but per the red truths, anyone who goes out of a room MUST leave a trace, given the "perfect seal" truths. And since you've eliminated any possibility of anyone being killed outside the rooms, someone must have entered, and therefore exited the rooms. So basically, what you are asking us to do is assert that someone entered the rooms and didn't enter the rooms at the same time.