Ahh. If your idea is that Gerry hadn't realised that if Kate would have necessarily seen the open shutter upon walking the long way via the front and the story suddenly had to change between his statement and hers via communication over lunchtime... I'd thought of that, but it still doesn't make sense to me.
I doubt that if there had been a staging of the window that it would not have been taken into account. All Kate had to say was that as she passed by the window on the way to entering the flat from the front that she noticed that he blinds were up. It wouldn't have changed anything. If Gerry had decided to stage raising the blinds, there's still not reason to enter via the front. Even less to state - in the SAME statement - that he'd exited via the patio door which was how Matt went when he checked.
I really don't think that anyone was terribly awake when that statement was taken.
I don't think Gerry considered the 'open shutter' idea at all. I think the fact that he said he used a key, Matthew did not, then Kate did is the crucial bit, because it makes little sense.
I think Matthew was simultaneously giving evidence, therefore 'key stories' had not been discussed. Kate gave her first statement in the afternoon, which does not have the key, so I do not suspect 'key rigging'.
Gerry was awake when his second statement was taken (around 10 May) and his first action was to verify that his original statement was correct. Then to change it.
Just for the record, this does not make Gerry guilty of any crime, with perhaps the minor exception that a witness is required by Portuguese law to answer all questions truthfully.
It was not a good way to get the hunt for Madeleine progressed. If, statistically, the first persons suspected in a child disappearance are the parents, then Gerry was acting in a manner to deflect attention away from an abductor, and onto Kate and himself. A potential bum deal for Madeleine.