RE: insurance company's payment of a claim 1st to Medicare and then to me if any is left

I am on Medicare and broke my shoulder in a fall at a church. They have a non-contestable $5,000 Medical Coverage Condition in their policy. The insurance company claims they MUST pay my Medicare bill 1st before paying me any of my out-of-pocket expenses. My total Medicare-covered payment will probably exceed $100,000. Therefore, would any liability claim I filed and won have to exceed that $100,000 before I would receive anything? I.E., wouldn't the 1st $100,000 of ANY claim I was awarded actually be on behalf of Medicare, who would otherwise have to pay that amount?