Can blue cross be reimbursed on a settlement from an auto insurance uninsured motorist policy?

This will depend on regulations for different states as well as policies. In most cases automobile medical payments will pay before health insurance will be responsible for remaining expenses from an automobile accident. If Blue Cross was billed and paid first before finding out that their was payment due from the person's auto policy then yes, Blue Cross will have to be reimbursed for the payment they made.