That is the remote we are referring to, yes.
Past versions of the Apple TV have been built such that they ignore 3rd-party remote signals by IR while the Apple RF remote is still paired. It is possible that this could have changed with the new revision, but you would need to consult the owner's guide for the product (or with Apple directly) regarding that point.
Aug 4, 2015
Dec 5, 2015
There seems to be some disagreement among reports of how this is working. We will reply to multiple users individually below.
What you describe is what we would expect from any Bose product, but your post doesn't mention exactly what you are using. Can you let us know what Bose product you are having success with? (and what remote code are you using if applicable)
JasonG: The basic commands should work as expected. It is ambiguous from what you wrote: Are the Play, pause, stop commands you mentioned the only commands that work? Or are these the commands which do not work?
Teaching Bose remote commands to the Apple TV would require putting your system in to "teach mode". Instructions for that are found here: (https://www.soundtouch.com/KnowledgeCenterView#!/feedtype=SINGLE_ARTICLE_DETAIL&id=kA1330000004O1DCA...)
Note: this process will use the IR emitters on the front of the Bose console to send the signals. The included external IR emitters can also be used for this. However, the IR emitter on the front of the Bose remote will not send the codes you need for this process.
The latest console software version for the Lifestyle v35 is 021001. If you haven't already updated to begin with the instructions labeled "Before Downloading" on this page: (http://worldwide.bose.com/downloads/en/web/home_entertainment_system_overview/page.html)
At this time we don't have any information about when another update for that system would be available or whether it will contain new codes for the Apple TV 4. The information regarding "teach mode" we gave to JasonG above also applies to your system. It may be worthwhile to empoly the Universal remote features on your Apple TV.