Alex,
Here is the full case. I don't think it resolves who the men were. There is a sentence about the bodies later being in a cemetery chapel, so I assume they were (at least initially) buried in a nearby cemetery, possibly the main cemetery in Brixen. Have you tried searching British War Cemeteries in Northern Italy for men with a date of death of Oct 1, 1944? Just looking at Google maps you can see Brixen is close to the Austrian border. I am not sure if any POW camps were located that far north, which makes the escaped POW idea a little less likely. Brixen is on the railroad route up to the Brenner Pass which was being bombed around that time, so the concept of a shot down air crew is also quite plausible. That also makes the concept of a failed SOE/OSS mission seem plausible. See, for example here:
https://www.cia.gov/news-information...phen-hall.html
There is also a mention in the trial record that there was a warning of "parachutists about" i.e. in the area. (There is nothing to suggest the three men were actually parachutists, but it does not say they were not either.)
War Crimes Case:
https://www.legal-tools.org/doc/d3e3b0/pdf/