It sure seems that way, according to Android Guys. They claim competing eBook apps such as Kobo and Aldiko don't appear in search results when using the Amazon Appstore on a Kindle Fire tablet. Additionally, eBook reader developer BlueFire claims that while his app is listed as Kindle Fire-compatible on the Amazon Appstore, it too fails to show up in search results on the device.
We've not heard of many apps mysteriously not showing up in the Fire's app list (presumably Amazon had lots of time to work on ensuring most apps on its store would be compatible) for a lack of compatibility, so if this does turn out to be true, we can probably assume that Amazon made a conscious decision to keep competitors' apps out of the hands of users.
However, let's not forget that the Kindle Fire does come app sideloading-ready, so you can get your alternative-eBook reader fix on that way. And that even Google keeps competing app stores (think of Amazon's book business like an app store) out of its own Market, which is why Amazon's Appstore has to be sideloaded onto your phone or tablet. As Amazon is the US's number one retailer of books, digital or otherwise, it only makes sense for them to keep competitors from cashing in on a device the company sells at a loss.
Amazon should probably speak up on this, regardless - if only for the sake of full disclosure. Their curated app store model, and their semi-walled-garden device do seem to suggest Amazon wants to keep a lot of control over the end-user experience on the Kindle Fire, so this doesn't come as a surprise to us. Especially considering that the device's entire profit model relies on users buying digital content from Amazon, and not someone else.
We wouldn't call it shady, per se, but it definitely does paint Amazon in a slightly more Apple-y light.