The claim by many foreign-policy sophisticates is that while Syria’s Bashar Assad may be awful, at least he’s fighting Islamic State. The reality is that Assad is devoting most of his military effort to fight Sunni opponents of his regime other than Islamic State. Until he defeats those other rebels, Islamic State is useful precisely because it makes him appear to be more tolerable to many in the West.

Well, now we have new evidence of Assad’s complicity with Islamic State. On Wednesday the U.S. Treasury Department sanctioned...