I'm saying that they didn't take enough measurements to measure the effect of it they didn't take all of the measurements they'd want to, and the measuring they did wasn't accurate enough, they didn't even know (apparently) which gauge they used for some of the measurements. On top of that, they don't know how well the balls held their air pressure. Did I miss anything?
I am actually an engineer with a background working with applications of the ideal gas law (and some other gas laws), and there are a couple of things beyond the uncertainties that BballTim has listed. I am being a total devil's advocate to refute the NFL because I don't believe them anymore. I don't know what happened but I enjoy trying to shoot down the NFL's case (which isn't hard because it has a lot of holes).
The first has nothing to do with gases but when leather gets wet, it relaxes or stretches a little. All the balls would have a different level of moisture content at the time of being measured and the leather would be different in every ball. This doesn't necessarily favor the Pats but their balls would have been a little wetter when tested at halftime than the Colts balls which had a little longer to dry. This is not a big difference but we are talking about fractions of psi. We are talking about 0.5 psi out of a total absolute pressure of about 27 psi or 2% so something small can be making the difference in these measurements
The other thing that can make a difference is that as balls are pumped up, the air inside gets hotter. The pump takes air at 0 psig (14.7 psia or absolute pressure) and compresses it to say 13 psig (27.7 psia) so that it can go through the needle and into the ball. This small amount of air will be hot per the ideal gas law and will mix with the cooler air already in the ball. So if the refs added a little air to the Pat's balls, the air in the ball at that moment would be a little hotter than equilibrium (room air) and the cooling effect would reduce the pressure even more.
If the Refs took a little air out of the Colts balls, the air in the balls is expanded a little and cooled a little, reducing its change in temperature and resulting change in pressure. This type of thing could contribute to the fact that the Pat's balls lost more air pressure than the Colts. I say "could" because I have never seen a description of what the refs did with the balls before the game.
And my final thought (for now anyway) is if there was a camera on the bathroom to record that McNally went in with the balls for 90 seconds, shouldn't there be film to show any other time he had gone in? If he had been at work all day and didn't go to the bathroom, wouldn't that make the idea that he just went to the bathroom more plausible? And if they had film of him taking a leak say 30 minutes earlier, that would destroy his story. Since the NFL has leaked every other detail true or not, if they had him in the bathroom earlier, I sure we would have heard about that.
It seems reasonable to me that he would take a leak before heading out on the field. He is probably required to stay on the field and would not have a chance to run back in before halftime. I know I take a leak before I go to my seat when I go to games.
For anyone still reading this long post I want to explain gage pressure vs. absolute pressure. When they quote 12.5 or 13.0 psi, they are implying that this is gage pressure or psig. Gage pressure means the difference between the pressure you are measuring and atmospheric pressure (which varies but averages 14.7 psia at sea level). Pressure gages can only measure a pressure relative to a reference pressure so gages inherently reference atmospheric pressure (it is right there and easy to reference). The point is that pressure gages of the type used are not highly accurate and real gases do not behave exactly as ideal gases. You are comparing a inaccurate measurement of gage pressure to a somewhat simplified calculation of absolute pressure-temperature changes so 0.5 psi of bias (about 2% of the absolute pressure in the ball) is a really small difference.
Why would McNally go to all this trouble to release an almost immeasurable amount of air from the balls? You could barely get the needle in and out quick enough to limit the release of air to the amount we are talking about.