Take a look at Shmuel I and Shmuel II (I Samuel and II Samuel) from the Torah/Bible and you will see that God was pissed at Saul, not for killing the Amalekites (men, women, children, and animals), but for sparing the life of their king and best cattle.
Modern day Israel likens Palestinians and Iranians to modern day Amalekites. Killing of men, women, and children is not only permitted, it's encouraged. Pictures of dead babies or innocent bystanders have little effect on Israelis because it's what God demands.
Now you know what you're dealing with. Israelis frequently use the term Amalek to justify their actions.
I'm not sure I totally agree, but that's only from lack of understanding. That's to say, I don't know enough about this subject, but you may be correct and I'll keep an open mind. After reading about the sin of the Amalekites, it does look like a good possibility