For the IRS, it doesn't matter how you value something - it's only the market that matters. I believe that in order to show a different valuation, you need to demonstrate "fair market value" by showing how much it should cost to purchase the item on the open market. Since the only legal market I'm aware of for purchasing AA miles is directly from AA, and they charge $625 for 25,000 miles, this is most likely how they arrived at their value.

Congratulations on winning, and good luck mitigating your tax liability.