It's complicated.

As I understand it, the short form is that the same laws that keep a corporation from taking photos of you in public and using your face and name to sell their product also make it hard for a movie company to tell the story of Erin Brokovoch or Queen without their permission. Not impossible, just "hard" -- so hard that it's often cheaper to just get permission and be done with it.

Part of it is likeness rights, part of it is defamation, and part is just the threat of an expensive lawsuit.