Faulty Apple TV remote?

sounds likely

best way to rule out the tv's hdmi-cec being the culprit Consumer Electronics Control - Wikipedia

would be to try to connect the appletv box to another tv (your own 2. tv, or tv of a friend, relative, neighbor or well-wisher), because it would be a bitter pill to purchase a new remote only to have it display the same behavior

Did you try restarting just the remote, using the button combination as described in the related article?