I forgot to mention this, but a massive hole that I've pointed out already, is that Ted Wells assumes the Patriots balls all started at 12.5 PSI.  The refs didn't record it, but they claim to have measured the PSI.  But there's video proof/other refs who have said in the past, that pre-game checking of PSI is not done very carefully.
If you don't know what the football PSI started at, how can you know how much it dropped?  One popular theory from way back, is that the Patriots try to sneak in under-inflated balls past the refs to check (similar to how the Packers try to sneak over-inflated balls past the refs to check).  If that is true, then the starting football PSI was lower, which combined with the cold weather explains the halftime PSI.
		
		
	 
That video you keep referring to establishes that 
one ref, before 
one game, didn't check PSI very carefully.
It does not establish that that same ref doesn't check PSI very carefully before 
all games.
And it definitely does not establish that 
all refs don't check PSI very carefully before 
all games.
In this AFCC game, PSI was clearly a point of emphasis.  There wasn't some cursory "eh, close enough" check done.  My recollection of the report is that Walt Anderson checked all 12 balls, found a few over 12.5 (in the 12.7-12.8 range) most at 12.5, and two below 12.5.  The two below 12.5 were inflated to 12.5.
The starting point for the balls was 12.5, or slightly higher in a few cases.