Issue is that this is actually neither.
Black Dragon Grief wouldn't work based on the character of the skill argument(that is, it forces fleeing). Petrify would. This violates all logic as they're the same skill based on mechanics, more or less.
Black Dragon Grief and Petrify both don't work. This violates all logic as they don't work like that at all, completely different based on character. In both cases it makes no sense somehow.
Or, if Black Dragon Grief does work, why not Persona 3/4 Fear, which causes people to randomly flee but not enemies? Suddenly it's decent odds ID when it connects, just delayed.
How about statuses that have the character of making someone run from a fight despite not having any such mechanical effect? Why not say Kain ring-outs when he jumps? He's sure as hell above any reasonable vertical boundary. How about Pokemon Fly? That takes you across continents, there's a decent argument for that sure as hell having a sideways sweep more than a ring's size. What about 4D Pocket, which gives you a game over but gameplay-wise only does so if you're the only person left? You come right back. Are you even out of the ring if you're in an alternate dimension? Is there a ring there? There could be, we don't see it. Are you out of the ring if you're somehow folded dimensionally to another area and come back, and if so, does Supernova instantly ringout people?
How about interference while we're at it, that's a good clusterfuck argument we haven't had in a while.
Or is this argument about testing against PCs? Why, yes, why don't we test things on PCs. We'll start with the FF games where defense stops cutting in PC against PC damage. I mean, if you want to go that road, go for it, I have nothing against it, but consistency is consistency. There's also a bunch of removal skills that work fine against enemies but never will against PCs(Dejeon in FF7 and Invite in FFT for example, though there's probably a DL-applicable few floating around. I'm not an encyclopedia on move properties, I'm afraid. Yet!), so this can cut both ways.
Now, granted, there are some hiccups based on current views-things like FFX Threaten and FF6 Control are taken as their (useless) performance against PCs. In the case of Control there's some secondary headaches(there's literally no mechanics for Control against PCs. Enemies pick skills from a list just like confusion. If you somehow got control against a PC you'd get a blank list. I suppose you can argue it would just allow full skillset control except it doesn't let you do that to monsters. So...how the fuck do you go with that one?), but Threaten...eh.
But the point is that it's not like it's totally fucked up anti-logic that makes no sense here. It makes sense on one level. Going with "intuitive" logic like stoned people are dead people and that's nothing like running....well, then you have to define your intuition with everything else based on appearances, and that's a hell of a road to go down. One that has to led to arguments at least as weird as the ones I stated, and some far weirder. If you believe in it, go with it, I love it when people have weird views...but don't get mad when people don't agree.
Edit:
For the record I hate both views, intellectually. They never mesh. There's no logical way to reconcile them(in-game there's not either, you just use suspension of disbelief, just like how you ignore how many times you get shot and stabbed.).
I just go with the mechanics one because it opens less of a can of confusing worms. I like my views to be consistent and by god that's hard to do with RPGs; That is, to have logical thought based on appearance, and have it resemble the game mechanics even vaguely.