Installing other apps won't give them access to you wallet, the OS enforces code signatures, so only apps signed by the same author can access keychain data created by that author's apps.

Breadwallet is open source and anyone is free to fork the code and make their own wallet, which is what Robert Genito of wall-of-coins did here. He integrated it with their exchange service. I know him personally and have no reason to think there's anything untoward here. He asked permission to use the code even though it's open source and he didn't have to.