No, you do not have to pay a deductible when you were at fault and the party that you damaged makes a claim against your property damage liability coverage.

What you have been told by others is correct. Your $500 deductible is due when you make a claim against your own policy for damages your car sustained and are going to get repaired. Usually this means placing a claim through your collision or comprehensive covers. For example if your car was damaged in this accident with the parked car and you placed a collision claim through your own policy then the deductible amount would be due.

If you have specific questions about how this claim will be processed by your insurance carrier you should contact your agent who knows the terms of your policy and the guidelines of your insurance provider.