They present one deal publicly, then renegotiate every Free App of the Day deal depending on whether or not they feel that the it is to Amazon's advantage. The Angry Birds get paid, the small local guy does not. This is predatory, though not illegal, and shows that they fundamentally misunderstand the ecosystem they need to foster in order for them to do well. If they were the only game in town, this might work for them, but they are not.
I have only anecdotal evidence, but it seems to me that the Amazon Store is used to grab free apps and nothing else. It's not compelling for users or developers.