Unfortunately, I'm not so sure that is true but TBH I have no first hand info either way.
Update: Just to clarify, I am asking a question about the Win8 Kindle app, not any other Kindle app. The Kindle app which runs on Windows 7 is not the same app. They are different apps entirely.
The thing is, I have found several reports that indicate that the Kindle app for Windows 8 never supported personal documents, meaning that Amazon has not taken away any abilities. For example, the blog Neowin reported on the updated when it was released a few weeks ago, and several commenters made remarks along the lines of:
ouch still no sideloading of mobi files
I also found threads on the official Kindle support forums that imply that the app doesn't have this feature (here, here) as well as a review of the app from January which says basically the same thing.
I have not been able to confirm this myself (no Windows 8 thank FSM) , so I am going to leave this question open to anyone who would care to answer it based on first hand knowledge of using this app.
Can someone with Windows 8 clear this up, please?