The private parking company won't have CCTV, the store might. Initially though approach Sainsbury's to get it cancelled, you are a genuine customer, be prepared to prove you went twice, people will say anything to get out of a PCN so they won't automatically believe you.
The fact the store is in the middle of nowhere isn't very relevant, Sainsbury's won't be putting in enforcement for the fun of it. The supermarkets only do it where they deem there is a problem.