You are assuming this is a sociopath doing the killing. If it is a muslim fanatic, your analysis is wrong. A muslim's motivation is religous in nature - he is doing it to get his 72 virgin reward in heaven (that big whorehouse in the sky). Thus, to him, it is a moral act, by the will of his satanic god.
I agree completely. The point of fact is that in either case the person is hardly insane.