This link that Walpole posted a while back makes a TON of sense:
http://finance.yahoo.com/news/physicist-emailed-us-explain-exactly-143048032.html
This physicist posits that:
1. the Patriots hand over their footballs, with temperature (and thus pressure) raised from the ball preparations.
2. Because the football exterior is a poor conductor of heat, the excess temperature/pressure inside the ball is maintained for a while. (SumnerH made this point a few hundred pages ago - this makes sense if you assume that the Pats' prep work goes on for an extended period of time ie long enough for the whole ball to equillibrate to a higher temp.
3. The officials test the footballs and perhaps even have to DEFLATE them to 12.5.
4. Over the course of the game, the footballs cool to ambient temperature and their internal pressure falls.
Even if Belichick suspected this of happening, it probably wouldn't have served him to lob a direct accusation at the refs - although might explain why he said additional investigations outside the Patriots were needed.
Reasons why Pats footballs might have behaved differently from Colts footballs:
1. Officials measured Patriots footballs first (before they had cooled to ambient), then Colts footballs.
2. Colts use different prep/storage methods.
3. Colts ask for balls at 13.5 or do not specify any particular pressure.