This is a very good question, because under ordinary circumstances HIPAA, which is a federal protection, would not allow WT access to your health information unless directly authorized. However, if a JW allows access for the HLC, it may be one of those grey areas (like talking to a medical professional who is submitting for insurance reimbursement, which automatically authorizes disclosure of diagnosis and procedures.) So it seems quite likely that allowing the HLC in as a "counselor" would allow sharing of information within their "network," and by extension, WTS.
However, I don't believe the HLC has ever been given the actual medical records, but more like they were present as a more authorized chaplain, able to sit in on (with patient permission) on consultations and directly advise family members on decisions to be made.
Remember that HLC pre-dates HIPAA, so who knows what the situation was prior to '96. FWIW, I don't remember my father ever storing any kind of medical records during the early days of HLC.