The Customer? I don't think so. The contractor is always responsible for work performed under contract. If they get a permit and inspection or if they get no permit or inspection. Even with a permit and inspection the the local authorities assume no responsibility for the work performed.
What you get with a permit and inspection is knowing that you are working within the law and that there is another qualified person ( the inspector) that certifies all visible work is code compliant at the time of inspection.
If something does go awry the passed inspection would go a long way toward helping to verify that it was a code compliant installation. In court having an expert unbiased third party is about as good as you can hope for. You are never really free of responsibility, that's for the court to decide.
If you have ADT fire and security in you home, are they responsible for a fire, or burglary? NO. They did not send the burglar or start the fire.
My job is to install everything to code and use only UL approved parts. The permit is the customers responsibility. Every installation I do is on film. In court a picture is better than any persons opinion.
If a job passes inspection and the house burns down because of a loose connection or nicked wire the inspector didn't see. Who is responsible then? The contractor? The inspector? The agency that issued the permit.
Just because you get a permit and get it inspected dose not mean you are free of responsibility. So the work, not the permit is the contractors responsibility. So don't get all warm and fuzzy just because you get a permit.
In order to do change a panel or do new construction you need a permit. I have no problem pulling a permit. I do it whenever I can. I will not refuse work over a permit though.