I got an app rejected once because it lacked a “Window” menu. I had never thought of putting one since the app could only have one window and didn’t handle documents. The HIG was cited.
So, following the HIG, even when it doesn’t make sense, as long as your app is not broken by it, it’s good sense. If your app can’t work within the HIG (for example, a game with a custom UI) then Apple might be willing to let it go, but for most cases the HIG is law.