I would have thought that an inspection pertaining to a permit for electrical work, would have to be done by an electrical inspector or am I wrong?
Yes Work under permit is done by an Electrical Inspector.
This survey is not that work. I as a municipal employee would not go to a house and do this kind of an inspection as it could attach liability to the city.
These inspections are done by contractors and in my mind I'd never do one for fear of liability. They are intended to be a complete and detailed evaluation of the entire electrical system. Anyone doing this is always in danger that any shortcut they took could result in liabilities especially if they are in any way naive or trusting short cutting employees.
I don't see permits involved unless the contractor also fixes what they find. The challenge is to keep this work to qualified persons. I have read enough general home inspection reports to know the variability in their competencies. Major faults being missed and petty things over emphasized. An electrical contractor is the right person for electrical surveys.