This always happens with comic/movie/other fictional universe debates. We can all accept that a fictional world doesn't operate by the same *exact* rules as ours, and there is a certain suspension of disbelief, to an extent. But within that fictional universe, certain rules are implicitly or explicitly defined.
Boundaries...Jedis can jump really really high using the force, but they can't just use it to fly. Neo is faster and stronger than any agent in the Matrix, but he can still bleed, and die (temporarily, anyway) in it.
And then, inevitably someone says "it's just a movie/ doesn't make sense/ check your brain at the door before you go in" or something like that.
Nothing is wrong with debating what the boundaries are within the established rules that are shown within the universe. That's part of the fun. You may take an explanation of the filmmaker as the final word, but that's a lot of "tell" instead of "show"....bad storytelling imo to rely on extra-story features to explain something within the story, especially when you already made so much effort to establish the "rules" of how things work within the story itself.
Besides, Nolan's explanation from the special features, as well as costume designer Lindy Hemming's explanation in the The Dark Knight "making of" book are ambiguous enough that it can mean either explanation...that the cape is the backpack, or that the cape folds up into the backpack. Not to mention that they are talking about how it might have functioned specifically for the bat-pod scenes...not a BASE jumping scene.
Taking only the clues within the story we know that
1. the cape can be loose falling, or in a rigid shape when a current runs through it.
2. We also know that the cape is a velvety matte black no matter what form it's in. The light refracts off of the backpack like it's a smooth hard piece of plastic, ceramic or armor, there is no velvety matte or flocked look to it, as the cape material has in both it's loose and rigid forms.
3. We also know that the backpack (two of them in fact) appear in a solid-state form in TDKR without being attached to the suit, without any current running through it.
I fully admit, it is quite nerdy to analyze it to this level, but for me it's clear. The hard backpack in TDK and backpacks in TDKR are not the same thing as the cape, which is even pliable when in it's rigid wing form.