Sure. This doesn't seem so surprising to me; after all, the number of possible answers you may choose from for the question "Which bit do you want to flip?" is precisely the same as the number of possible answers you may choose from for the question "Which book do you want to specify?". (That's not a proof of sufficiency, mind you (the proof is the construction of the appropriate Hamming code). It's just reason to not find the result particularly counterintuitive.)