Well, my main counterpoint to this would be that some people aren't particularly good actors, but they can have phenomenal story ideas. Giving those story ideas a compelling, exciting, enthralling performance is rather different from having them in the first place, and just because someone can't shift their voice or convincingly act, doesn't mean they should be told they can't really express the story ideas they have.
But notice what the person you responded to was saying: in D&D, and games like it, this association is extremely strong. To have more "we are living through an interesting story", you usually have to have more "Alas, poor Yorick! I knew him, Horatio". This isn't true of all games, and many games that followed the style of Apocalypse World--those "Powered by the Apocalypse", PbtA--specifically do separate out "I am an Actor upon a Stage speaking Lines and Emoting" from "I am part of the process of unveiling and advancing an interesting story".