Legally, Non-custodial parents ARE still entitled to medical records .... period.
All dad should need to show is a birth certificate and ID confirming he is the person listed on the birth certificate.
This is true but...
Often the father is NOT on the birth certificate.
Parents can loose parental rights for a variety of reasons.
I would agree he should have access unless she can provide reason why he should not. The onus is on the parent trying to restrict the access.
A variation on this sometimes occurs with parents who have lost parental rights and the child has been put under the custody of the grandparent or other relative. Usually in that case Child Services is in the picture, but sometimes not.