I think it’s less of a clean split than you’re making it. The statements I listed show both. Sometimes leaders stress, “he was one of our own,” sometimes they stress how “this is not who we are.” Neither is pure ownership nor pure cowardice; they’re rhetorical tools for different purposes: unity, deflection, grieving, or political cover.

If anything, the very fact that they have to insist “this isn’t us” suggests they’re already grappling with the same discomfort you’re pointing out. It’s just a more polite way of saying “we wish it had been someone else’s problem.”

Either way, it’s not coded anti-immigrant language.