Did you see Belichick's press conference this afternoon? It's on the Patriots website.
He went into excruciating detail about the tests they did this past week.
He had two very funny lines,
First after he explained something he said he's not a scientist, he's not an air pressure expert and "I'm not the Mona Lisa Vito of footballs." Which made me laugh out loud.
Then, while answer some dumb reporters question about how vigorously they rubbed the balls during preparation he said he didn't know, but it was vigorous. "We're not polishing fine china here."
I think that this is going to come down to sloppiness in the procedure by the referees. I think they generally took a "Close enough for government work." approach to testing the footballs and didn't gauge them as they are supposed to.