To say what I'm trying to say in a different way, Jimi Hendrix and Guns N' Roses didn't exactly cover Bob Dylan, they played his song as if they wrote it (with explosives). The tribute thing was a rockstar movie reference, but another good example would be DarkStar Orchestra (they'll learn an entire Grateful Dean show note for note). Musicians can play someone else's song exactly like the original, or wildly different in a number of ways so the idea that people playing original music vs covers is the important distinction in how they chase toan doesn't hold up. RATM did Renegades for Christ's sake.
I might propose that the question is more simply whether someone is trying to hone their own tone vs replicate someone else's. Another bifurcation could be that the tone of a song, or section is determined more from a songwriting perspective. I have an envelope filter on my board for exactly one part of one song because it belongs there for that song. That song is an original, but I'm also covering some commercial country songs with octave/fuzz so clearly not covering the tone there.
Duff isn't going to change his tone to play a cover song, but they are an original band. His OD tone is his tone.
I'm not saying it's a definite line between cover and original. Just a general observation. People that are liking their amps OD are more apt to use it to make music.