Or in this case, perhaps, it's more like "cutting off the noses of Russian orphans in order to spite the U.S. Congress."
I thought your phrase по принципу "раз Америка бомбит Сирию, мы разбомбим Воронеж" seemed very apt, too. I can't think of an English equivalent, but I guess one could say "If the Soviets invade Afghanistan, the U.S. will bomb Seattle," or something like that. It sounds very Kubrickian!