It's the 6 DBs sitting in zones that caused Brady to hold the ball. The 2 LBs were practically on the LOS, either rushing or dropping back into a zone. Although Pats adjusted by setting picks on the DBs. Cowboys need to adjust to that adjustment by not having the corners in man to man all the time. Mix it up.
Yes, there are ways to combat the picks; however, when they tried have the CBs on the same side switch-off in past years based on the routes, Claiborne always made the wrong decision. Scandrick and Claiborne would end up covering the same receiver and the other one would go uncovered. Scandrick could then be seen screaming at Claiborne and telling him what he should have done.
I think they had tried to keep things as simple as possible for Claiborne this season. I think simplicity is the reason that he is playing better; although, he is not really playing great. I reviewed the defense against the Saints in detail and Claiborne was probably the biggest contributor to the failures of the defense that day.
Nevertheless, they still need to try something to combat the pick plays. A 2 man zone is one option. Another option is tighter press coverage which makes it more difficult for the receiver setting the pick to get between the DB and the other receiver. The downside is that if the DB does get picked off, then he won't be there to make the tackle when his man catches the ball.