How to serve a fish filet: skin up or down?
I think it depends on which fish, and the way it's cooked. If it's steamed,poached, or en papillote, fish skin can be quite unappealing to some diners, and, as you say, the conventional way to eat the fish would be to lift the flesh from the skin, especially if at the same time you are parting the flesh from the bones.

But if it's an oilier or meatier fish, pan-fried or grilled, the skin can be deliberately crisped, in which case it's intended to be eaten. (This, again, is much easier to eat if the fish has been filleted from the bone before cooking.) In that case, it is sometimes more attractive, and keeps the skin crisper, to serve it skin-side up.