That happened on the opening drive of the 3rd quarter, which from memory was a drive that they chewed up something like 8 minutes of clock before the giving it up on downs.
It was a weird decision, but it also was in that weird part of the field where if they punted it's most likely a touchback, and they'd have gained all of 10 yards of field position, but if they went for the FG and missed, Giants would've had it on the 45. I do get the thinking there. If they score a TD, and waste another 3ish minutes doing so, they'd have been up by 11, with the Giants likely only getting the ball again 3 times. Another Pats TD afterwards most likely ends the game.
Also for the record, Maroney was terrible in that game as well.
Like I said, that Giants defense was a terrible matchup for the way the Patriots were built that year. Pressure up the middle while rushing 4, and allowing them to sit back in proection.
You'll never convince me that Bill got outcoached in that game, the Giants played the perfect game, and had a 1/1000 play happen to set up the win, much like the Edelman catch against ATL.