It's per design that the app can still open the camera app, to receive a picture/video which you can make with it.
The camera permission is for access to the camera of the device itself, if an app has the camera permission it can, even if you don't take a photo, see what the camera(s) of the device see. Even without showing you - you'd still be able to notice the green light at the top right corner, though.
If an app just asks the camera app, the originating app doesn't receive any pictures from the camera hardware, unless you actually take a picture with it. So you can always just cancel/close the app without worrying about it.