As an app developer myself, I think this level of secrecy is unjustified. You will never get your idea off the ground if you are as secretive as this. Revolutionary ideas are rare, they are usually iterations of previous ideas, and for this reason I don't sign NDA's at the moment unless necessary. However..
For your case, if you get as far as Apple review your app is already developed. You have such an advantage on the market that anyone who learns of your idea has a pretty major disadvantage already. If your idea is as good as you think it is, then when your app hits the store, provided it is properly presented on the app store, it will be such a hit with users that you will have the advantage of being first to market. An idea is worth nothing, your competitors have the disadvantage of having to carry out the real work of executing that idea, making it better than yours, and overcoming your first to market advantage.
Against your case is the following clause, which says that Apple can develop competition to your app. I believe that this clause is necessary for Apple to evolve their products without being stopped by small players - for instance, so they can develop their "Notes" and "Weather" apps without being stopped by Evernote and Dark Sky for instance.
The clause :
Here is item 11 of the Apple Developer Agreement
Apple Independent Development. Nothing in this Agreement will impair Apple’s right to develop, acquire, license, market, promote or distribute products, software or technologies that perform the same or similar functions as, or otherwise compete with, any other products, software or technologies that you may develop, produce, market, or distribute. In the absence of a separate written agreement to the contrary, Apple will be free to use any information, suggestions or recommendations you provide to Apple pursuant to this Agreement for any purpose, subject to any applicable patents or copyrights.