"Piracy isn't stealing" doesn't require a qualifier. It's objectively a separate, lesser crime. That correlation is just the result of effective, aggressive marketing that conflates the two. It was so effective that everyone misremembers the "you wouldn't steal a car" ad.
Thanks for that trip down memory lane. I was just a child when I saw that, and my first thought was "but... But when I steal from someone, they don't have it anymore. If I download it, they still have it"