No, it's because it's a vasoconstrictor. As a person who is both a caffeine addict and a past sufferer of angina pectoralis, I can testify that the headaches caused by caffeine withdrawal and the headaches caused by nitroclycerine (a vasodilator) are one and the same.
Vasodilation is not necessarily chemically induced, but it is a common-enough proximate cause of headaches (and some other forms of pain) that using a mild vasoconstrictor in addition to an analgesic is more likely to make a general-purpose pain reliever work effectively.
Vasodilation is not necessarily chemically induced, but it is a common-enough proximate cause of headaches (and some other forms of pain) that using a mild vasoconstrictor in addition to an analgesic is more likely to make a general-purpose pain reliever work effectively.