This has been an interesting thread to read. The proof of abduction theory will always be a point of contention. From my perspective, there is no proof of an abduction. Even the shutters, whether they were open or closed still doesn't support or dismiss the abduction theory. Whether the shutters were even open seems to be another point of contention.
The problem here is the contaminated crime scene. That's not to put blame on anyone for this because the PJ were looking for a missing girl and it is unlikely at that early stage of the investigation they considered the apartment a crime scene. Plus it didn't help that people were coming in and out. That didn't really help the investigation when it became clear that it was a likely crime scene.
This isn't clear to you? ok ... Kate KNEW instantly that Maddie was ABDUCTED.
instantly she announced it! then they all go back to search the apartment where the twins were left and still asleep to hopefully find that:
1 Maddie shook off the gang and returned from the abductors
2 the abductor was in no good hurry and decided to stay on a while hiding in the apartment..
You see my point? why would they search all over the apartment if they already KNEW she was ABDUCTED.. hmm?
...and then why not someone run to reception shouting my daughter has been abducted? help phone the poilice !!!all very calm and had a good look round messing up the apartment and those'abductors' fingerprints that were no where to be found all got wiped with the 'searching' Oh dear what a bummer.