two of us collided into each other backing up from a parking lot  - ontario.
Does each individual pay for their own repairs - paint job only. Other person says I was at fault. I say the opposite We exchange names etc.. No one was hurt and  a colleague told me each person is responsible for their own repairs. Is this the case?

call your insurance agent & make a claim, usually they decide who is at fault with all the facts they collect. I'm not sure how it works in Ontario, but that's what happens here in BC. I just had an incident in December where the person said they didn't do it, I made a claim, they checked out the damage to both vehicles. A little different as I was parked & he backed into my bumper & did some damage with his trailer hitch. 

I believe the rules of the road that if you are backing up you are at fault. Since the other driver backed up at the same time ( both cars in motion?) you are both at fault.  I'd bet your insurance would find it 50/50.  If the cars hit back bumpers than the drivers didn't do proper shoulder checks.
Off topic a bit- this is the #1 reason we always back into any parking spot, including our own stall at home. It makes leaving so much safer since you can see everything. I wish more people would park like this- we see so many almost hits from this exact scenario. 

Something to check:  I can assure you there are very few parking lot accidents in which both drivers admit they were backing. Your insurance company would have to complete an investigation to gather facts and determine if they have enough evidence to support either driver's version of the accident. An independent eyewitness (NOT a passenger in either of the vehicles) can usually clear things up quickly. Also check with the store where the accident happened and verify if they have videotape of the parking lot. Many do and liability can easily be determined with a video of the accident. 

Read more: http://wiki.answers.com/Q/Who_is_liable_when_two_cars_back_into_each_other_in_a_store_parking_lot#ixzz1wJ9VjEOy

in a parking lot.

whether we are hit by a car, big person or shopping cart..if the damage is enough to put in a claim ICBC follows though if you have the coverage.
Copied:

Comprehensive auto insurance can cover things like flood damage, theft damage, fire damage, attack by dragon, ballistic missile attack, tiger mauling, and other general acts of god. It will even cover you if a tornado decides to pick a fight with your Ford F-150 and winds up depositing it on the roof of the local Target. Comprehensive, as the title implies, covers all damage that can happen to your car outside of a "collision." Collision coverage helps when you hit a tree, a person, another car or accidentally drive into the side of your Aunt Martha's condominium complex.