Rather than argue, I'll just state what I consider to be dark, which I feel is the official way that it should be applied, and leave it at that. That being: it can't be dark unless these serious things are actually focused on and addressed, rather than just being kicked away like a small stone on the path. I mean, with how many near-deaths that occur in various media, and the amount of deaths that are just mentioned (i.e. dead parent(s), usually for character development background), we'd be dealing with a shitload of dark labels all over the place. (Even something like the Little Mermaid, or the Lion King.) But we don't, because it's always about the prevailing features. Let's take the story with the sick boy that needs medicine to live, but won't take it, and Ranma ends up getting involved. On its face it concerns a serious topic and, while it can be dark, if such a thing were common enough in its given medium (Ranma 1/2), at best it can be considered drama in the series. However, considering the comedy and slapstick, it's simply can't be even that.
A couple of examples of what I consider to be dark, off of the top of my head, would be movies like... Eye for an Eye and Strangeland.
And, yes, I do realize that I'm addressing it as a whole, rather than in bits and parts. The way that I see it, is, if it's like looking up at the sun, where you can't see the sunspots even when aware of their presence, it just doesn't matter. Majority rule, and all that. In this case, a minority of a minority of a minority. And the minority, as far as I see it, isn't even dark.
Now, edgier, on the other hand... That makes more sense, to me, since I think it's actually applicable. Though I haven't seen all of the anime, so I can't determine whether I think the anime or manga is edgier.