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

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. 

I’m not sure about the “pressure” , but leaving the double doors open at the center back of my listening room creates a noticeable (to listeners) and measurable (REW software) difference to the positive. Exactly as another poster described by reducing reflectivity and room modes. 

If your room is small to even large if you are throwing over 90 db + pressure levels opening a door can be a good thing  for eventually room reflections  will create distortions and overwhelm the room ,it has happened to me and my room is 30x16x8 and I just sit 12 ft from the front of the speakers I can’t sit further back or I would  I have gym equipment and dresser. In front I open the door and the room sounds not as congested ,when the spl levels are under 90db which is most of the time playing rock in the mid 80db level then it it’s ok, I have Bass busters acoustic panels behind and to the fist reflection s to the side and wall to wall carpeting , no windows except at 30 ft away  , no matter how expensive the gear is your room has its limitations with hard reflections at higher spl levels.