Since Kelly's time, the NFL has instituted the "no-chuck" rule, allowed QB's to ground the ball outside the tackle box and created other rules to protect QB's in the pocket, and has started enforcing pass interference, and as a result, the passing game has opened-up significantly. Beyond that, the Patriots were 6th in the NFL in rushing.
As for his "insane" games in the 2nd half, he had 4 of them. They were against the Dols, Jets, Raiders, and Cards. The Raiders were ranked 10th against the pass. Pretty impressive at first, until you realize they were ranked 31st against the run and no one bothered to pass on them. Meanwhile, the Cards were ranked 22nd against the pass, the Dols 25th, and the Jets 29th.
But again, even still, his 21 TD passes were 10th in the NFL, despite his great WR's, great running game, and bad competition.