Campbell
Relaxed Intensity
This is quite a reductive view of fiction! Take any story--A Tale of Two Cities, Star Wars, Parable of the Sower--keep the setting and the minor characters, but change the protagonists. Give them different personalities, motivations, and skill sets. Would the story change in a pretty fundamental way? Probably!
In an RPG, and adventure path provides some of the elements of a story, but it is incomplete. To make it complete, it requires characters. Who those characters are, the choices they make, and who they become can significantly alter the end story. How and the degree to which the adventure changes will depend on the style and temperament of the group.
It would be like describing Lord of the Rings by saying "Well there was this evil ring and yada yada yada some people (doesn't matter who, could've been anybody) threw it in a fire and the world was saved." The journey is the whole story!
I mean it's fairly obvious to me that people are making comparative claims. When they say Adventure Paths feel passive and characters feel interchangeable it's in comparison to other sorts of play. They are essentially saying that they want their characters to matter more than is typical of Adventure Path play.