> It was my understanding that it is included because many people taking headache pills don't actually realize that they are caffeine addicts and don't recognize the withdrawal symptoms for what they are.

If true, I would find that rather disturbing.

Many things about the OTC drug market in America are rather disturbing. 26k people per year are hospitalized from acetaminophen poisoning, and about two die every day. It's the scumminess of the pharma industry, with less adult supervision.

As with many things, all the suggested reasons apply, in different proportions for different people. The caffeine may help with vasodilation-related symptoms. It also may help with any other caffeine-withdrawal symptoms, if present. And it may create a slight new dependence – as with the other painkiller ingredients, which can contribute to 'rebound headaches' with persistent use. Adding an addictive yet legal substance to your product is rarely bad for repeat business.

This may be a useful side-effect, but the original reason is the one given by your parent.