Doesn't matter, YOU have not had any claims and YOU have not had any accidents, and neither have YOU claimed on your policy. Your parent has (unless there's an unresolved dispute about who was driving come renewal time I suppose). Chances are they will also have their own 'named driver' no claims, which is lost, while your own 'proper' no claims remains intact.
If you add them as a named driver next year they may bring the cost up, but your premium should be unaffected.
Since it sounds like your insurance company is getting involved anyway, may as well call them to confirm that this is what will happen.