Why they trust the first court case, but not a second case with equal/better access to evidence is worrying but worth thinking about.

The simple answer is that it's hard to change your mind, since once a belief gets formed it tends to become entrenched in various ways. There's a sequence and an upcoming book about the specific ways in which that's true, but some which seem most relevant in this case are:

1. Confirmation bias. Once someone forms a belief, all the new evidence that they see gets interpreted in light of that belief so that consistent evidence seems solid & important and inconsistent evidence seems dubious. Even if someone's initial belief was based on the first verdict, by the time the contrary second verdict comes in they feel like there is all of this other evidence alongside the first verdict.

2. Thinking in narratives. Once someone forms a belief they come up with a story for why others disagree with them (e.g., they're just biased in favor of the sympathetic pretty American woman), and as long as new events can be fit into their storyline they aren't much of a challenge to the existing views embodied in that narrative.

3. Identity. Once someone identifies with one side of an issue, they'll associate that side with all sorts of wonderful values & virtues (e.g., standing up for the integrity of the Italian justice system against the meddling foreigners) and they'll see changing their mind as abandoning their side and failing to live up to its values & virtues.