Consequently, many people are under the impression that when the download the free app of the day, they are doing the devs a favor and earning them 20% of their list price, and I have absolutely seen people in public forums run around advertising when an app from a dev they like is a free-app-of-the-day, telling people to help support said developer by downloading the app even if they don't really want it because said developer will receive some financial support from the download.
The fact that all of the above is bullshit and that Amazon has been secretly negotiating that down to 0% of the list price with the admonition that the developers cannot tell anyone they aren't getting the 20% everyone thinks they're getting tends to indicate that Amazon is aware of this confusion and exploiting it for their own gain.
Do you seriously imagine that members of the public are attracted to the Amazon Android App Alliteration Store because they think Amazon is a more charitable and supportive firm than Google, and shows greater kindness to the ramen-chewing developer? I feel pretty comfortable in asserting that the vast majority of people don't give two hoots about what arrangement exists between publisher and distributor. Do you go to the movie theater and decide to watch a Universal film because their producers are nicer than the ones at Paramount? Do you grade other products/services you buy by the providers' corporate social responsibility score, or the credit terms extended to their suppliers? Of course you don't. With a few exceptions (mostly symbolic) you are wholly ignorant of such things, and rationally so. You assess products and services based on whether they fill your needs at a reasonable price.
I don't run a whole lot of apps and as a result have not got around to using the Amazon store, but non-industry members of my social circle have mentioned that there's 'a free app every day' there. I suspect that if I asked what return they think this nets for the developers of said apps they would just give a me a funny look.
Many people do go out of their way to support independent musicians or indie game makers. It's not unreasonable to believe that there are people who want to help support small mobile development shops.
"A broader userbase" that doesn't pay anything isn't "help" by any stretch of the imagination for a number of business models.
They certainly derived value from the transaction. By giving away a free app a day, Amazon drives customers to its marketplace, and its brand. To suggest that Amazon's intentions are purely altruistic is naive.