Medpay

I was in an accident last year. I have Anthem Healthkeepers Medicaid so the medical bills were processed by them at their contracted rate. I didn't owe anything because with Medicaid there is no deductible or copays. The at-fault driver's insurance company gave me a check for the full amount that Medicaid was billed by my providers...not the contracted rate but the full amount which is legal and also great. I have Medpay on my USAA policy with a limit of $10,000. Am I allowed to also submit those medical bills to USAA and get reimbursed up to that limit of $10,000? I live in Virginia so double dipping like that is allowed I believe. Just wondering if USAA would reimburse me the full billed amounts like the at-fault driver's company did or if they would only reimburse if I actually had any out of pocket expenses (which of course I don't since I have the Medicaid).