But the door wouldn't have actually been open or ajar or unlocked. Nobody could have proven otherwise if John had said he found a door unlocked or not completely latched.
They also don't have to worry about them checking for evidence at that door because there would be none. Just like there is no intruder evidence in JonBenet's room, the kitchen, the basement, or on her body. They never staged the evidence of an intruder, they staged the acts that they thought an intruder would do. Why would an intruder climb out a basement window when he could just walk out one of the doors. Why wasn't that staged?
...again, yes and no. If JR said, "I found this door unlocked," then it would have to be unlocked when the police examined it. What possible reason could he give for locking it again, once he'd found it unlocked?
And then we have forensic evidence: the police can tell if the door was unlocked using a key or not, for example. They would expect there to be some signs that someone had inserted a key from outside. If all the latent prints on the doors were R prints, and there was no sign that any of them had been disturbed, that's another bit of evidence.
Or to put it another way: the "intruder," even if he had a key, would have either a) left prints of his own, or b) smudged prints the R's had left during normal use of the door (say, if he were wearing gloves). There would possibly have been either prints or smudges around the lock, and there would definitely have been either prints or smudges around the doorknob, which the intruder would have to have turned in order to enter.
So you see, the very fact that there would be NO evidence of an intruder is, in fact, evidence: evidence that there wasn't one!
Same goes for the intruder's exit point: even wearing gloves, the intruder would have blurred the existing prints on the interior doorknob when he opened the door. Even if the police bought the idea that someone who had a key managed to enter without disturbing evidence on the door, I think there'd be some suspicion over the lack of evidence of either entry or exit.
I think JR was smart enough to know that when you start trying to stage 'evidence' of an intruder, you open the door (no pun intended) to lots of awkward questions. And the Routier case must have been 'out there' by then; I remember it distinctly myself, and yet I'd forgotten how close in time to the Ramsey case it happened.