I am at a loss why you would think an HI should not be using a non-contact tester. I am willing to bet it is in their training to do so.
I don't think the use of a non-contact voltage tester is part of their training. Trouble-shooting is not part of a home inspection.
A home inspection is limited to the critera of the inspection, list of items to be checked. I can't think of a single item that would require a non-contact tester.