I think the point is that its a creative process so there's no right or wrong way to do it. The job title may suggest otherwise if you think of, say, a structural engineer where if he does it wrong the bridge collapses.What's your point here? That it shouldn't be called mixing engineer or sound engineer? In that case, I think that's an uphill battle. That's the name of the profession, what's the point of debating that?
Example - 'Raw Power' - Iggy Pop & The Stooges. Two mixes, some prefer the original Bowie mix, some the later Iggy remix. (Bowie for me). No right or wrong.