Based upon this scenerio, the vehicle making the right turn is At Fault due to unsafe lane change / careless driving / possibly reckless driving. BUT...depending upon the state you are in, a parking lot is considered "technically" to be private property and therefore the offending driver may be protected from being cited by the police.
If you're backing up, generally, you're the one at fault (regardless of how stupid the other driver is). However, some insurance companies may differ.
strike slip fault
Firstly, this should be reported to your insurance carrier. Usually, accidents on private property (parking lots, private roads, government facilities, etc) are "No Fault", which means each person sustaining damage makes their own repairs at their own cost.
Andreas fault.
You are. Since you were unable to stop in time it means you were following too closely.
Transform fault
Rocks on either side of a fault move along the surface of the fault.
Worn front wheel bearing(s)
The San Andreas fault
a judge in an American court makes the decision as to who is at fault for an auto accident. some states have "no fault" meaning in an accident all parties involved are given a percentage of the accident's fault
Most of the time this will be a 50/50. If there is Video evedence or a witness that says one or other car was being careless or driving to fast or there is other evedence that could change. One of the things to look at is did the backing car back into the side of the other car or did the backing vehical get hit in the side and how far down the side? If you have evedence of this you might convince the judge and your insurance company who was "At Fault"
BOTH drivers are in violation. The other driver for making an illegal turn, and you for driving without due caution or following too closely.