This is a valid concern. In games where we give up a TD on the opening drive, we are 0-4. In games where we hold the opponent to a field goal or less on the opening drive, we are 3-0. That's a pretty remarkable disparity.
Considering the players' and coaches' expectations for how many points our offense will generally score in a game, which are probably somewhere between 13 and 24, getting down to a 7-0 lead on the first drive of the game would have a pretty significant effect on the psyches of the offensive and defensive players, as well as the coaches.
Think about it. The defense gives up 7 points immediately on the first drive, knowing that if they give up more than 20 points we're USUALLY going to lose the game. So, what do they do? They press hard, and play as hard as they can trying to give the offense a chance to catch up...and eventually pressing like that wears on them if the offense isn't doing their job, and we have seen the defense fall apart on key drives because of that. On the offensive side of the ball, they also know that we're not scoring more than 20-24 points in the game even if we're having a relatively good day, so they go into opportunistic mode, where they start passing the ball more because that is what the defense is generally giving us. I think they WOULD run it, if they noticed that defenses were dropping safeties deep into coverage and giving us the run, but defenses don't generally do that, so the offensive coaches and players seem to be convinced that being down 7-0 means you have to be more opportunistic than when you're tied or have the lead. Also, the opponent's defense probably plays with more confidence when they see the offense score on the first drive of the day, because they don't feel like their backs are against the wall and they can run downhill on the Phins and run their defensive game plan the way it was written.
Scoring on the first drive of the game has a pretty dramatic effect on the outcome of the game. I know that the Chargers last year made their way by scoring early and therefore changing the nature of the game to their favor.