What hypothesis exactly?
There are many ways of skinning a cat, I guess. The prosecution can prove the burglary was staged by inviting the court to draw inferences from the sheer improbability that a real, professional burglar would ever choose that window and from other evidence purportedly suggesting a scenario quite different from the lone wolf burglar one and that the inferences are so strong that scientific demonstrations are unnecessary. I see nothing wrong in principle with that, it's just that the application of the principle in this case gives rise to very weak (if any) inferences at all. I don't think the prosecute has to prove, in general, that what it is suggesting is not impossible*.
Is it possible for Nara to have heard the scream? I don't think it is so if I were a juror I would want that demonstrated for me if I were not to reject this part of the prosecution case (which I might still reject anyway for other reasons including her unreliability) but I don't think the prosecution is obliged to prove in any particular way whether she heard the scream.
*this may be too sweeping. We had a case of a guy who was found naked and dead inside a bag in his bath, itself within his locked apartment. At the inquest, evidence from an 'expert' was given that he could not have closed himself within the bag, the expert having tried repeatedly to do it himself, proving it was not suicide. Laughably, right after the inquest, some kid showed how to do it easily. Leaving that aside, suppose they found a suspect and accused that person of murder, using CCTV, DNA forensics, fingerprints and all sorts. On whom would the burden have fallen to show it was impossible for the guy to have trussed himself up? The party alleging impossibility or the crown as part of its burden of closing all avenues of reasonable doubt?
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Yes, what you are describing could be (or was) the prosecution strategy. But the defense did counter what it thought was that strategy. Did the judge reasonably account for the defense counter and the prosecution allegation (or hypothesis), and reasonably decide between them? Or did the judge realize that the prosecution hypothesis was not viable, and so assumed the role of prosecutor, providing his own hypothesis, which the defense was not aware of and thus could not rebut, and the judge then made his hypothesis the judicial finding.
Have I described the situation accurately? If so, is the judgment in the case fair in this respect of whether or not the break-in was staged? And if it this element of staging a break-in is important for the conviction, is it fair over-all? And of course, if it leads to an unfair conviction, there is a violation of Convention Article 6.
How did Nencini treat the issue of the alleged staged break-in? (I actually don't remember.) Was it fair or unfair in itself, and was it fair or unfair in terms of Nencini's judgment of conviction?
ETA: With respect to Nara and the "scream": the defense attempted to challenge the possibility that it could have been heard, using audiometric testing, IIRC. The judge (Massei) denied the defense request. What was the reason for the denial? Was it fair or arbitrary? Was the result important for the conviction? If yes, then if it was arbitrary, the conviction is burdened by that unfair denial of a defense request, and there would be further grounds for ECHR to judge a violation of Convention Article 6.
ETA2: The prosecution, in proposing something which is physically impossible as a basis for conviction, will generally be countered by the defense. Perhaps all the defense would do is bring in an expert to state that there is a physical impossibility. Does the prosecution have evidence that contradicts the defense argument? But the argument must be fairly adjudicated, and the judge can of course bring in experts to help resolve differences. But I don't believe the judge can play the role of prosecutor; if the prosecution case is not viable, then the defense must be acknowledged as "winning", the judge cannot substitute a new prosecution theory or hypothesis for one that has failed. And certainly not one the defense has not had the opportunity to evaluate and rebut. Do you see otherwise?
