Very likely (your remote suspicion).
Users frequently report issues similar to this (content playing, channels/app being automatically installed) whenever the lower left ad is displayed on the Home Screen.
Doesn't happen to everyone so likely something in the setup is causing the Roku to sense the Play/Pause button has been pressed.
The lower left ad is not nornmally always present though (will come and go with different promotions), although unfortunately with the holidays, this ad is likely to be more present for a while.
Maybe try placing something in front of the 4800, or hide it behind the tv and see if that helps with some errant IR signals it may be receiving. (when hidden, your 4800 will communicate with the Roku remote via RF/wifi direct so does not need to be visible/have line of sight).
