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I'm trying to reconcile them having iron clad proof of the time being wrong, iron clad proof of the postal police arriving, and the judge that is biased towards their side plainly disagreeing with them.
You are misunderstanding the situation. This is not mathematics so there are no proofs.
The situation as it stands is the following.
The clock is ten minutes fast is the only evidence presented in court. This is based on a technician's determination by comparing the CCTV time to the accurate time.
Bongiorno raised the alternative way of attempting to calibrate the time using the phone call but all of that is based on a hypothetical to ask a question. Bongiorno herself can state the time of the call as that is evidence from the phone records which are attested to as accurate by another witness who collected them but she can't enter the argument of connecting the car and the phone record as evidence -- only a witness can do that. She asks Barbadori and he says he did not do anything with these.
The purpose of Bongiorno's questioning is to plant the idea that Barbadori should have done this. To plant the idea that there was an alternative and that the alternative might have come to a different result which make Barbadori look less credible -- something he doesn't need much help with since he is not well prepared and comes off badly. In the end though this is still not evidence just a lawyer intimating that evidence exists and attempting to hurt the credibility of a witness.
If the defence wanted this to be evidence they would need to put up an expert and by asking that expert questions have the argument becomes part of the evidence. It appears that the defence choose to not do this. This is based on a completely lack of any evidence that it happened despite attempts to find it and more importantly because they asked at the eleventh hour for permission to do so -- thus logically implying that they had not already done so.
This request to enter the argument into evidence brings us to Oct 9 2009 when there was a procedural meeting of the court to request additional evidence and experts be allowed. Massei disallowed this. So the postal.pdf which was prepared to show the court a glimpse of what this new evidence would establish was only used at the procedural meeting of the court and not at the actual trial.
It is certainly possible that if Massei had allowed this new evidence that the new evidence would establish that the clock was slow. We will never know because the witness was not allowed to testify and more importantly the witness was not subject to cross examination.
The known facts though make the possibility that the postal.pdf would have been convincing extremely unlikely. There are two reasons for that. The first is that despite Barbadori being a shaky witness the simplicity of the method used by the technician to calibrate the CCTV clock does not allow for error. I simply can't imagine how someone would screw up something so simple.
The second reason is that for the defence to establish their argument they must establish that the car in the video is the car that required directions. I don't see how that is possible. There is simply no way that can be done. Maybe the defence figured out a way that I can't think of but we have no evidence of that.
As such we have to conclude that Bongiorno making the hypothetical argument in cross-examination was intended simply to create the appearance that Barbadori did something wrong but failing to pursue this avenue. Bongiorno likely knows that the argument doesn't stand up if examined but for the purposes of damaging credibility it doesn't have to -- juries are not thinking about this and they just register that there was something the witness could have done that he didn't and that is bad.
With the postal.pdf again the reason for requesting it was legal strategy. The defence had already come to terms with the fact that the verdict was going to be guilty. As such the strategy changes to one of having Massei make as many procedural decisions as possible. Every procedural decision and every piece of evidence excluded increases the opportunities for the appeal. As such they asked to allow the postal.pdf knowing it almost certainly would not be allowed but hoping to gain that refusal as something they could object to later.