Shecky,
I had similar damage but for a different reason. My DS always had 2 stuck pixels but I could live with that. It also had the slightly loose/spongy feeling touch display but could live with that. After a month or so it developed a crack on one hinge. Since I heard it was only cosmetic I didn't really bother to do anything about it. Soon, the other hinge developed a fine crack. Still, didn't bother to fix it. One day when opening it up the darn hinge popped off. Looked very similar to your photo.
Was very disturbed because I was worried that Nintendo would think I had mistreated it. I'm a 40 year old man with no kids. I've treated this thing like a baby. Also kept in a nice case and never dropped. But there's no way to actually prove that, I suppose.
Anyway, Nintendo begrudgingly replaced the unit. They said they didn't usually cover damage like this. Oh well. By the way, the replacement unit has a stuck pixel as well :-) But I can live with it. But if and when next hairline hinge crack appears, I'm sending it back immediately !
Oh, and I do have a second DS (my wife and I wanted our own) that I bought at launch as well and it has had zero problems ( knock on wood ).
Eric