From the TNG episode "Darmok", where Captain Picard has to learn how to communicate with an alien through shared danger.
From DS9, the decades-long Bajoran resistance to the brutal Cardassian occupation.
From the Voyager episode "Message in a Bottle", where the holographic doctor has to go outside his comfort zone in order to recapture a federation starship from the Romulans.
From TNG, the friendship between human Geordi and the android Data.
From DS9, the friendship and subsequent romance between Odo and Kira
From Voyager, Janeway's insistence that Borg drones are still people.
Fatal flaw: Versus mode (PvP) with random strangers is almost always awful. Only well-balanced teams of roughly equal skill can have a good time, which is unlikely when playing with randos.
As opposed to the co-op campaigns where it's OK if some players are better than others because we're all on the same team and a good player can carry several n00bs.
It could certainly be used as evidence in your favor. Whether it by itself would be enough to exonerate you would depend on things like the evidence against you and how much weight the jury gave to your records.
Yeah, I worked in a few affordable housing sites and the OP looks like something the on-site social workers cooked up.