You could also do a true backup camera which displays the video feed in an embedded display in the rearview mirror. That's a more elegant solution if all you are looking for is a backup camera and don't want to replace your radio or have a dashcam.
I am a huge proponent of dashcams and I encourage their use, but they are not the best solution if what you truly want is a backup camera.
I am not disputing the value of dashcams in a variety of circumstances, and not just the instance which you mentioned. I run one in every car I own. As I previously very clearly stated, I am a huge proponent of dashcams (for your reading pleasure here is my thread about installing a dashcam *with rear cam* input capability, btw: http://www.hyundai-forums.com/233-rb-2012-accent/224953-modding-my-accent-well-sort.html).But you want to have a recording in case you get rear-ended by a truck and the truck gets no damage and drives away, the recording would capture the face and the front facing camera can capture the license plate if it drives off ahead of you... makes getting insurance money to fix everything much, much easier.