Ovinomancer
No flips for you!
Oh man, I'm an idiot. I didn't realize this was an author stance versus director stance discussion. It's the same concept that underlay the argument about 4e martial daily and encounter powers. It's much harder to justify Int 5 geniuses with debilitating circumstances if your focus is on "inhabiting" the character rather than generating dramatic play.
Well, I don't know about that, as I never had any problems with 4e and daily/encounter powers. I also don't have much issue with the refluffing in general. I do have an issue with the specific choices of example here, and how they're defended, because the main one (LOL) uses her narration to break other game mechanics. I'm fine with a refluff that stays within it's swim lane but when it starts impacting other mechanics in ways that break those mechanics, I do have an issue.
So, I guess I'm in the middle? Like the card using casters, but more of the Kid's, where it's a fiction sub for the casting implement, not the actual source of the magic like ElfCrusher's example. The former is a fun roleplaying change that stays in it's swim lane -- it doesn't change other mechanics. EC's, though, does, and relies solely on players not abusing the loophole they've created. It also has issues, as noted, when interacting with outside mechanics that may remove the player enforced limitation on the mod. That's not good.
I've played mildly insane characters (a conspiracy nut most recently) and used that character background to enhance roleplaying failed rolls. If I didn't know something, for instance, I'd make up a conspiracy story about it. My character would 100% believe this to be truth, but it was wrong. If the mechanics of that game system had a zone of truth, my character could fail the save or make the save, but he'd have the same story, which was both wrong and 100% true in his eyes. That's internally consistent, and doesn't break other mechanics, and has a high fidelity. An example where, on a failed check, you know the real answer (and really do know the real answer), but don't tell anyone because of your delusion, doesn't. It breaks because it relies on the player to not abuse it, and it breaks when subjected to an effect that removes the player's ability to not abuse it, which, in this case, is as simple as a ZoT.
Refluffing can be tons of fun. I do it quite often as a DM and player, and I encourage it at my table. I don't encourage godmodding (great term!), though, and make sure that any refluff has a narrative fidelity so it doesn't break other mechanics and doesn't solely rely on the player not taking advantage of it.