Doesn't mean that he only knows how to fly planes or helicopters either. I've known plenty of pilots qualified to fly both. You're right that it's often very convenient for the character to be qualified for both, but it's not some insane notion that the movies are trying to pull over on you. Many pilots are actually able to pilot both. They rarely flash multiple licenses and inform everybody about each license they hold before flight. Much like you might not tell people "In addition to this car, I'm also fully licensed separately and legally with a CDL, motorcycle and hovercraft, too!"
Well, true, but in some cases the pilot is a pretty ever-day person. Getting a Private Pilot's License costs around $4-$5000, a Rotor-craft License costs double that and up.
Not out of realm of possibility for someone to have both but, probably pretty darn rare.