You have some very strong misconceptions about the AppStore.
Apple won't reject your app because it is opensourced (just add the open source license as your own license). BUT Apple will reject your app if one of the copyright holders complains. Including the copyright holders of the original open source code. That's not because there would be anything wrong with your app (only some expensive lawyers can decide that) but because Apple doesn't want to be involved in anything that could go to court.
If you publish your app as opensource, the copyright holders might complain. Or they might not complain. Whether they are right or wrong, I couldn't decide. However, if you publish NOT as opensource, then 1. they WILL complain and your app WILL disappear from the app store, and 2. If they sue you for copyright infringement, they will win.
In addition, note that you can't put opensource code on the AppStore for money. That's because Apple on one hand says that any payment is not for the app itself, but for the license to use it, and GPL on the other hand says that you can charge any amount for the app itself, and a reasonable amount for the source code, but you can NOT charge for the license. Therefore, any open source app on the app store must be free (as in free beer).
@Joshua: Nobody knows if Apple can or cannot permit it, but if a copyright holder complains (and the open source authors are usually copyright holders), then Apple will remove the app. So are you sure that a lawsuit actually happened? Note that for any open source app, you can demand the source code, and recompile it on your own computer, without needing any keys.