Yes, this is absolutely normal for any camera (including the $15 one in your iPhone). The red eye is caused by the LED (not actually a flash) being located too close to the lens. What happens is that the light from the LED bounces off of the back of the eye and then right into the lens. The angle has to be just right in order for this problem to occur. Your only option is to use an external flash (if one exists), buy a real camera, or use the phone with the flash turned off. Of course you can also remove the red eye with various apps, too.
To see how this works in real life, hold a flash light while looking into a mirror. The angle from which the light comes from the flashlight equals the angle from which the light reflects off of the mirror. If you get the angle just right, you can shine the light right into your own eyes. Move the flashlight up/down/left or right just a little bit, and the angle will be off enough so that the light misses your eyes. This is what you need to do with any camera in order to prevent red eyes.