I guess the answer is when operating in a displayed menu the CHAN/PAGE button should always be PAGE. Even if the menu is a channel itself.
And there is the problem in a nutshell. Our DoD menus are considered to be both channels AND menus.
I must be the only person bothered by this, because I never get any responses when I post this complaint, but I can't for the life of me understand why the designers have chosen to make these channels (with channel numbers and some channel-type behavior).
These should be menus, with no channel numbers and no behavior that remotely resembles channels.
All this confusion would then be gone. The ch UP/DOWN buttons would behave the same as they do on all other UI menus, and that would make sense. You still have the picture in picture in the top right, so I don't think anything is taken away by using this approach.