Yes, for Kindle books, this is indeed the case.
As perverse and non-sensical as it may seem, Amazon require you to purchase Kindle books either from a Kindle device - or by using the Kindle Books webpage on the Amazon website. Once purchased, books can be downloaded from your Kindle Library to your Kindle App.
https://www.amazon.com/gp/help/customer/display.html%3FnodeId%3DGDZF9S2BRW5NWJCW
Amazon have deliberately contrived their Kindle App to allow download of purchased books - but will not allow you to purchase books directly from the Kindle App. Amazon likely have a commercial interest in forcing you to purchase books in this manner (perhaps in encouraging you to purchase a Kindle Reader) - and only they have the ability to change App functionality.
Any representation that you wish to make needs to be directed to Amazon. One day, if enough customers complain, perhaps Amazon will change their current policy 🙂