It's no secret that the Amazon Appstore for your Android device is part of the DRM associated with the content you download from them. If you uninstall the Appstore application you will find that applications acquired through the store, both free and paid, will stop working and let you know that the Appstore needs to be installed, and your Amazon account verified before the apps will run.
Amazon doesn't publicize this fact but they don't hide it either. It was covered by the technical press within a day of the launch of the Amazon Appstore. It really isn't an issue that you actually need to have the Appstore installed for applications to work; DRM is a way that developers can protect their investment, and if you don't want to have to allow this process, you can simply elect to not purchase applications from Amazon.
The problem isn't the required Appstore installation. It's the fact that not only does the Appstore need to be installed, but it also needs to be able to phone home at some unspecified interval to, apparently, re-authorize applications. And it doesn't matter if those applications are paid for or free.
Now this problem is likely completely invisible if you have the Appstore running on a phone, as there will almost always be a connection available for the store to use to check in, but with the growth of the WiFi-only tablet market, the need to check in actually becomes a problem, at least in the fashion that Amazon currently seems to handle it.
I'm not a stranger to devices needing to phone home for authorization. I‘ve been using a ZunePass for almost as long as they have been available and I know that I need to connect my Zune to my computer and allow it to sync at some point during my subscription period or I will get messages that content isn't authorized. But I also know that once I've allowed the Zune to sync this way I won't have any DRM issues related to the ZunePass until the subscription period has expired.
With the Appstore I've run into this connection issue on more than a half-dozen occasions in the four months I've been using an Android tablet. I'll have WiFi disabled, and when attempting to use an app from Amazon I'll get a message ranging from a very clear "Application not authorized" to less helpful, "Unable to reach the Internet" when an application fails to launch or some set of features fails to work within an application.
As I said earlier, I don't have an objection to developer's protecting their work with DRM, but I would like to know that I can use the applications that I have paid for, and it would appear that Amazon doesn't re-authorize their applications when you open the Appstore, something I do on almost a daily basis. Whatever the process is, it behooves Amazon to let users know that they need to check in, and provide a process for making sure their apps are authorized, so that they don't discover this while trying to use an application while on a long plane trip or in some other location where easy access to the Internet may not be possible.