I agree that in the first instance it was important to find out what had happened and to set the wheels in motion to find Madeleine, and as far as the main issue you mention goes ... of course they had an eye to covering their backsides.
However I find it extraordinary that one of the first things the Rebelo investigation found it necessary to do was to collate all these pieces of paper you mention and put the information contained onto hard drives.
You might be right about when this stuff was put onto hard drives therefore I am not going to suggest otherwise.
I had the impression that taking jpgs (photos or scans) of the statements was done shortly prior to the release of the files.
Photos (or scans) of statements is a truly awful way to getting the information cross-referenced.
I haven't seen anything in the PJ Files that suggests they had a decent system for analysing/linking whatever. Was the oldest such system called a Rolladex?
To be fair, I haven't seen anything that suggests SY is using more advanced technology than this.
Whilst it appears to me a couple of posters on here have the info cross-referenced on what looks like a spreadsheet. In lots and lots of lovely detail.
Maybe we should chip in and help them?
After all, we can tell when the police were called, can we not?