Practically speaking I would tend to agree with you. There's plenty of equations on line if for some reason you want to calculate the max error of your set up, but it ain't much.
I would however offer up a couple points-
We're talking putting a shotgun scope on a rifle- not the other way around. Under 50 yards I would expect my deer gun to put shot after shot after shot into one not so ragged hole, and any sighting error would indeed be measurable.
The math of the whole thing doesn't quite work the way common sense suggests. The error is increased more when shooting a distance that is shorter than the preset distance than when shooting a distance longer than the preset, so a scope set up to have everything "in front" of the preset does make some sense.
In a short range shotgun type situation one is much more likely to be snap shooting, resulting in a less precise cheek weld, and eye alignment.
Either way, in the real world, I do agree, I don't think the difference between venison stew and going vegan is going to come down to rifle vs shotgun scope.