Consider scenario 2: if some other runner touches home plate once and, on the plate, pivots directly to go run back to third base, he's fine, of course, because he never passed home plate.
Back to my first scenario, if the runner who missed third base pivots on home plate directly toward the third base dugout, he didn't pass home at all. He just pivoted off of home plate and walked more or less toward third base before realizing what happened and running directly to third base. You've said you have a viable appeal at home base here and I tend to agree, but...
Where do you draw the line between these two cases?