Yeah, this is what it boils down to. The American view of a right is as something which can't be taken away from an individual who didn't abuse the right, regardless of the number of other individuals who did. Rights are not and cannot be subjected to utilitarian calculations, and Americans consider gun rights as an embodiment of the right to self-defense.
In Europe and in developed countries outside the US, rights are malleable social constructs which can be redefined or restricted for the sake of some public good. The American nature is to react squeamishly to this approach, because allowing for a right to be curtailed a little bit could eventually lead to it being curtailed a lot, or for the same to be done to arguably more fundamental and uncompromisable rights. This caution is probably the reason our national government has managed 230 years without turning into what Russia is today, but the downside is that we miss out on a lot of chances at immediate social improvement.