Solid post - appreciate it. And as you noted, you had to pay the medical bill thru your on-board account, then seek insurance reimbursement. That happens even if you have purchased the 'insurance' thru Princess / Aon / carrier.
A copy of the medical records, Itemized statement of charges, and your final folio showing you paid that amount goes a long way for the insurance reimbursement.
been there, done that