Of course cases in which the defendant is found not guilty at the lower court and the prosecutor appeals is subject to an acquittal without referral. That is where the defandants have the balance weighted in their favour. There was a recent case in Finland - which follows Napoleonic Roman Law (German version) [as opposed to the UK, Commonwealth and USA Anglo-Saxon based adversarial common law]. A Danish guy was charged with the murder of two young German tourists on a cruise ship between Finland and Sweden, when aged 18, some 30 years later after his cellmates overheard him boasted about having committed the crime. He was brought before the court and charged. He was found guilty and his defence appealed on the grounds he had not been given a Danish interpreter at some stage. He won the appeal. The prosecutors appealed. The man was acquitted without referral. Do you see how it works? Had he been found guilty at the first instance court and he verdict upheld by the appeal court, there is no way the Supreme Court could acquit him without a referral back as the facts found at the lower courts still legally stand and it has no jurisdiction to change them. It was nor declared a mistrial or 'in the public interest' and it should be patently obvious that the reason a para 530 'insufficient evidence' is vanishing rare at this level is self -evident, in that 'insufficient evidence' becomes apparent at the preliminary stages not the Supreme Court stage! It is thanks to Bongiorno's hero, politician, Andreotti, that she was aware of this little used para, the last time having been Berlusconi, both found guilty and as upheld by both lower courts but used their political influence to wriggle off the hook.
Your post it too mixed-up (incoherent) for me to discuss of all its incoherencies or errors.
However, some of the errors are easily addressed.
Your first statement is:
Of course cases in which the defendant is found not guilty at the lower court and the prosecutor appeals is subject to an acquittal without referral.
Let's assume this is a discussion about Italian law, since Kercher was murdered and raped in Italy, and Knox and Sollecito were tried in Italy under Italian law.
Then one must consider the structure of the Italian judicial system and how Italian procedural law works in that system.
Your not clear which lower court in the Italian system you are referring to.
If a first-instance Italian court acquits an accused, and the prosecutor appeals the acquittal, that appeal is heard by an Italian Court of Appeal. That appeal court is free to retry the case if the judge believes that is necessary. The appeal court judge is also free to merely review the documentation of the first-instance judgment if the judge can justify limiting the appeal trial to that level of inquiry.
Under CPP Article 604, if the appeal court judge finds that there has been a nullity (a type of serious procedural error defined under Italian laws such as CPP Article 179) the case may be returned to the first-instance judge for correction or the appeal court judge may take measures to correct the nullity and proceed to a judgment under CPP Article 605. If no nullity is declared, the court of appeal judge proceeds to judge the case under CPP Article 605.
Under CPP Article 605, the appeal court judge is authorized to confirm or amend (change) the first-instance court verdict based on the trial conducted by that court of appeal judge. The case is not referred to a new trial, but the verdict may be appealed to the Supreme Court of Cassation (CSC) by the accused, the prosecutor, or both.
The CSC reviews the arguments of the appeal(s) against the judgment of the Court of Appeal for conformance to the legal requirements of CPP Article 606. If no appeal conforms to those requirements, the CSC rules the appeal(s) inadmissible and the judgment of the Court of Appeal stands as the final judgment of the case.
If the CSC finds that an argument of an appeal against the judgment of the Court of Appeal meets the legal requirements of CPP Article 606, it considers the legitimacy of that judgment in light of the soundness of the argument.
If the argument is so unsound that there is no defect in the legitimacy of the appeal court judgment, the CSC rejects the appeal, and the judgment of the Court of Appeal stands as the final judgment of the case.
If the argument is sound and thus reveals a defect in the legitimacy of the appeal court judgment, the CSC annuls the appeal court judgment in whole or part in order to quash the illegitimacy of that judgment. (BTW, the definition of "cassation" - cassiazone in Italian - means annulment - annullamento in Italian.)
The CSC then has the task of deciding whether the annulment may be made without referral or with referral. Any referral is to a different Court of Appeal than the one that delivered the judgment that the CSC had evaluated.
Since the CSC does not admit evidence or hear testimony, and ECHR case law requires that a trial is unfair if the defendent is not allowed to be present and, if desiring, heard before the judge, it generally cannot deliver a guilty verdict if the appealed judgment is an acquittal or dismissal. So it will annul with referral if it annuls an acquittal or dismissal.
If the situation meets of requirements of any part of CPP Article 620, the CSC is required to annul without referral and to issue the appropriate verdict. Thus, a really messed up judgment, like that of the Nencini appeal court in convicting Knox and Sollecito, will be annulled without referral with a verdict of acquittal required in accordance with Italian law.