I only watched the game yesterday, so I've had time to digest it a little. Thinking about it I actually 100% agree with the decision to throw, and 100% stand by my initial thought that it should have been a roll out pass. I no longer think a run was a good idea on 2nd down, so I don't hate the personnel they had in.
Basically they had time for two runs, or three plays provided at least one of the first two is a pass. Evidently to maximise their value they are going to pass at least once on either second or third down. Because Belichick knows this, if they run on second down, they lose any deception they may have had on third down, because unless there is a huge bubble BB knows to expect a pass. By throwing an incomplete pass on second down they are able to substitute, then open their entire playbook on third and have the best opportunity to score. If they don't they call a time out and getting another play. Unfortunately for this to work the QB needs to be able to throw the ball away if the TD isn't there, which obviously I have gone over already.