If the other driver is indeed at fault, your agent should fight for you to make sure the claim is paid through the other drivers policy. If not, a claim can be put in with your company and Progressive should go after their company in order to indemnify themselves for the payout (including your deductible depending on the % of fault). The term for this is Subrogation. If you want you can point it out to your agent using the Progressive website lol
Understanding Insurance - What Is Subrogation?