I would let him correct it first. If he’s not a contractor he needs to remove the claim of being a contractor. He should probably say that he is InterNACHI certified rather than state of Ohio licensed.
Contractor licensing is often very difficult to obtain. I would at the very least call him out on this. I spent a lot of money and time getting my contractors license and business license and it isn’t fair someone can just say they are a contractor to mislead a client.
If he inspects it and is not licensed, he will be liable to pay for the mistake (wouldn’t he?). Perhaps his license is expired and is therefore not popping up on a search. In California no license is necessary as a certification is valid enough. However, that is likely going to change sooner rather than later.
Seen it so many times it is sad! I found one Inspector in Texas claim they have over 20 years construction experience and yet they were only 26 years old. I suppose picking up loose nails on his Daddy’s construction job counts?