Fair market value is what a fair buyer would pay to a fair seller. You don't need proof that that is actually what the charity received for the items. For example, if you buy a shirt for $30 and it is new with tags, but the charity sells all clothing items for $4.99 regardless of condition, your donation value can still be $30. You don't have to account for the price the charity gets.
Most of the time, what you paid for something that is new with tags will be a good indication of fair market value. I can always imagine hypothetical exceptions: for example, if you pay a high price for a designer handbag and find out it is counterfeit, the fair market value is its actual value, and not the price you paid. But generally, you can use the price you paid.
