Auto Insurance Claims: parking lot accident NYS, parking lot accident, middle car

Question
The other day I was involved in an accident as I was pulling out of a parking space.  It was straight in parking.  The entrance to the parking lot would be to my right rear.  There are 3 spaces.  I was in the first space to the left.  A car was parked in the middle space.  The right space was vacant.  I obviously check all my mirrors, as well as behind me and to the right and left before I proceeded to back out, cutting my wheel to the right.  I would be backing behind the parked middle car.  Next thing I know I'm being hit be the car pulling into the 3rd vacant spot.  I have maybe a 3inch guff on the corner of my right rear bumper and the other party has a longer scraping on the left rear panel to the bumper.  We did not call the police but exchanged info.  The other driver stated "I saw you backing out so I sped up to get into the spot so you wouldn't hit me."  If they saw me backing out, doesn't it make sense to stop and wait.  I don't even know where they came from.  They must've come flying into the parking lot.  Anyhow, they contacted their insurance.  I don't feel I am at fault.  I am a commercial driver by profession.  I am required to attend safety meetings every month.  I know that excessive speed and lack of common sense was to blame....just looking for some other opinions or maybe some insight as to how the insurance companies may see it before I call back to give my statement.  Thanks.

Answer
Generally speaking, the party who is backing bears the responsibility if another vehicle is struck.
However, the areas of damage, the other driver's statement and the excellent description of the loss that you've provided will help to mitigate your degree of liability.  

If I were presented with this one as an adjuster, I'd likely accept no more than 50% liability.  The other driver obviously had the last clear chance to avoid the collision.

Good luck.