That doesn't mean that they can't do more de-escalation or take other steps, but the high prevalence of guns does seem like it would be a contributing factor.
(I realize this touches a hot topic (guns) but it's an honest question, and sympathetic to law enforcement.)
Switzerland (disclaimer; I'm Swiss) has also lots of weapons around, but if the police are ever shooting someone it's usually big news with investigations on whether it was really necessary.
From my laymen point of view, police training and holding them accountable to their actions is probably even a bigger factor than gun availability (although this is certainly a factor too). If I'm not mistaken, Swiss police training strongly encourages to back off if someone draws a weapon, trying to keep it cool, talk softly/slowly etc. It seems that in the US, the first hint of a weapon will result in drawn weapons by police and a 'drop your weapon'-shouting-contest; that's at least what seems to often happen in footage that ends up in the news where something goes wrong and someone ends up being dead.
Edit: One of the more memorable examples I saw was a video via NYT, where some guy was being arrested, tried to adjust his pants and was immediately being shot because the officer thought he was going for a gun. This is absolutely unimaginable in Switzerland; I would have to look it up for the facts but I think to remember a case where someone was shot holding (and threatening with) a fake-gun, and the officer who did so went to jail if I remember correctly.