Another interesting point is mentioned in Martin Grime's report when he talks about Eddie's alert to cadaver scent near the cupboard -
“What we have to be able to understand in a situation such as this is in a hot climate with the apartment being closed down, the scent will build up in a particular area. If there isn’t a scent source in here, i.e. a physical article where the scent is emitting from, any scent residue will collect in a particular place due to the air movement of the flat, the apartment and what I would say in this case is that there is enough scent in that area there for him to give me a bark indication but the source may not be in that cupboard, the source may well be in this room somewhere else but the air is actually pushing into that corner.”
So, what he's saying is the scent isn't actually sitting on something like a blood stain or piece of DNA would be. But because the scent has been in that apartment, it is still in the air and the air flow is just pushing it to towards an area with the least air flow, so that the smell concentrates there. A cupboard which is far from a window or door being a logical place it would collect and get trapped.
There's the possibility therefore IMO, that the origin of the scent wasn't even in the parent's room, but in MM's room. The sheets that MM lay on were not in the room by then, so all the dog is possibly picking up is residual scent left in the air, which by then could have spread everywhere given the traffic going on around the apartment in the prior weeks.