You definitely CAN browse video files while lying down.
First, make sure you are playing a video in Void/ Moon/ Space Station scene. Hold on the screen to drag it to the desired position while you're lying down.
Then if you call out the control panel and tap "Video List" , you can open the main menu and browse the videos while lying down.
You can also make the screen follow your head's position and orientation. Just simply press A/X/Trigger button to call out the control panel > tap Advanced Setting > Screen Adjust > Lock Screen, then your screen will track your head position and orientation.
Hope this helps.