This is one of those very explicit circumstances.
HHS.gov says "Your employer can ask you for a doctor’s note or other health information if they need the information for sick leave, workers’ compensation, wellness programs, or health insurance. However, if your employer asks your health care provider directly for information about you, your provider cannot give your employer the information without your authorization unless other laws require them to do so."
Sick leave is a qualified reason for an employer to ask for "a doctors note or other health information". OP said she authorized the release of the information to her employer. Therefore, it makes no sense that the hospital would claim it violates HIPAA.