“You have to open a door or window to let the pressure out of the room.”

Just think. If I played my stereo outdoors in the west with the speakers pointed east, my brother in Virginia might hear it. Not as loud though. 

Silly? More like dumb. Probably needs to open windows to air out farts that is affecting their brains. 

Total nonsense.

The description of releasing pressure makes no sense, but opening doors or windows will allow move of the sound energy to leave the room and could alter the sound the listener hears.  Whether this improves the sound or not, can only be determined by listening.

Interesting question. My system is upstairs in the bonus room. The room is well treated, however when my wife is home & downstairs, I am asked to keep my door closed. The sound that would travel downstairs with an open door is now bouncing around in my room. That has to make a difference, maybe good… maybe not. 
 

As I tend to do, I asked AI. According to AI, there is absolutely an effect. 

Door Open

• Effectively increases room volume.
• Allows bass energy and reflections to escape.
• Can smooth room modes and reduce bass buildup.
• Often produces:
  • Larger soundstage
  • Greater depth and air
  • Better speaker disappearance
  • Cleaner bass
  • More spacious presentation

Door Closed

• Creates a more enclosed, reflective space.
• Increases room gain and bass reinforcement.
• Often produces:
  • More bass weight and impact
  • Greater warmth and intimacy
  • Stronger reflections
  • Slightly more “pressure” in the room

Believe it or not, interesting question… and worth trying to see if you hear a difference.