For the record, I find the idea of a stranger removing the body unlikely in the extreme. I'd go as far as to stay that stranger abduction is more probable than body removal in this case.
If we are to take the statements of the T9 at face value, Madeleine was seen alive at roughly 9:10, then Matt entered the apartment again at 9:30.
The bed was not disturbed (and sexual assault is surely the most likely cause of DNA contamination?) There were no signs of a struggle, though how much of a struggle an almost 4 year old sleepy child could put up might not leave any signs anyway, but also no other DNA located in the the apartment or fingerprints, or signs of forced entry.
The only logical explanation is that an intruder caused her death, cleaned up the apartment then took the body. That in itself is just not logical.
As for the time constraint, you either have a 20 minute window, a thirty minute window, or an intruder hanging around and hiding during Mattt's check. All in the dark. Not knowing when someone will return.
On top of this highly unlikely scenario, you need to add in 11 separate ERVD alerts which were all either wrong or coincidental.
All of the above proves nothing of course. It is all possible. It just involves suspending your disbelief to such an extent that if it were a film plot, you'd be asking for your money back.