The interesting thing about the 37SR theory is how fast it took hold. SJL is taken on Monday afternoon and by Tuesday morning the police are organising a press conference in their canteen at 2pm to announce that SJL was seen at 37SR. This is before they've taken a single witness statement. The basis of the claim is not HR but the police themselves, who've decided this was SJL.
As the young people say, WTAF? The excuse is that this was urgent and they had to get their appeal out there but what about the risk you appeal for witnesses to something that didn't happen? The result would then be 2 weeks of silence which is what did happen.
Anything based on what the police wrote down is IMHO suspect because they were all into the 37SR assumption before they'd checked any detail at all. If they'd found that actually they had the keys all along, would they admit it?
The police can certainly be criticized for making assumptions and for jumping the gun, but in this case it seems to have been a reasonable assumption at the time of the initial press conference.
Suzy's diary said she would be meeting Mr. Kipper at 12:45PM outside 37SR. The neighbour, HR, told MG he had seen a man and woman outside--and seemingly looking at--37SR at the time Suzy's diary indicated she would be there. And MG's initial report to the police told them what HR had (apparently) told him. That was what the police thought they knew at the time.
As it stands, we can't even be sure HR was wrong. Or right. Or lying. Or mistaken. Or high as a kite on drugs and imagining things. We just don't know, and likely never will.
The forensics team was already inside 37SR on the morning of the 29th, *before* the first press conference that afternoon. So they already had access to the house. The door wasn't damaged, meaning they presumably must have had a key. Suzy was supposedly seen taking the key off the rack at Sturgis. MG supposedly hadn't been inside 37SR because he didn't have the key.
So where did the police get the key from?!? If they said it was missing when they had actually been given it by someone at Sturgis, they ran the risk that the person who gave it to them would contradict their story. Yet nobody has ever come forward, to my knowledge, and claimed to have found the key at Sturgis or anywhere else.
Either being given a spare set of keys by the homeowner, or finding the Sturgis fob inside Suzy's car and withholding that information for some reason, makes the most sense to me.
I could understand the police not wanting to admit they had made a mistake, such as announcing the key was missing when it wasn't. But given that the forensics team was inside the house on Tuesday morning, and the first press conference was on Tuesday afternoon, it would be truly bizarre to *mistakenly* announce that the key was missing *after* they had already used it.