I don’t know what the hospitals submitted. That’s a good question. Maybe somebody here knows the answer.
Whatever information was needed to verify place of birth would be on just the certificate if it was signed by a doctor, so there would be no reason for Fukino to refer to plural “records” if she was verifying birth place, unless the whole birth claim depended on supplementary information.
Regarding the fee, the part about “to amend his records” should have resulted in a “no records exist” response separate from the “access denied” if a fee was paid to see his birth record. They’re supposed to segregate the responses if different portions of the request require different responses.