As of iOS 8, apps do need to request access to the cameras. When an app on iOS 8 attempts to access a camera, it shows a system alert and requests the user to accept the access before the app is allowed. Denying the access will prohibit the app from accessing the camera.
For iOS 7 in your question, yes, an app can access either camera without requesting the user's permission (except in China as you found out). All apps have unrestricted access to view the camera feed of either the front-facing or rear-facing camera and take pictures/videos.
However, access to the Camera Roll to save such media does require the user's consent. Most apps on the App Store request access to photos immediately so as to not interrupt the user whilst they take their first picture, however this is simply to gain access to the general location for saving the media, not for accessing the camera itself. Apps are fully able to capture pictures and video from either camera at will without requesting permission providing it saves the media within the app's sandbox.