I am basing this on the fact that when most people take a breath and hold it they are not closing the airway off they are just keeping their diaphragm pulled down thus creating a larger volume of air in the lungs and keeping it there until the diaphragm is released.
At least for me, this isn't true at all. If I take a deep breath and hold it (mouth open or closed), I instinctively close my airway. This lets me release the pressure from my diaphragm so I'm not constantly "flexing" it - it just relaxes in a flexed position against the greater volume of air in my lungs. It actually takes quite a bit of effort to take a deep breath and keep that volume steady by holding your diaphragm down.