You are correct in that photographic �red eye� is due to the reflection of the flashlight on the retina of the eye. This is normally more pronounced in photos taken in poor light, since the subjects� pupil will be fully dilated.
The propensity to suffer red eye is somewhat dependent on the size of the subjects� pupil at the time the photo was taken and the angle between the light source (flash) and camera lens.
In olden days, this was avoided/reduced by placing the flash gun light source as far as possible away from the camera lens, thereby limiting the angle at which light could enter the eye and be reflected back to the camera.
Modern cameras, with a red eye reduction function, strobe the flashlight prior to taking the photo, thereby causing the subjects� pupil to contract and reduce the likelihood of light reflection from the retina.