Sorry, but that just doesn't stand up.
1. The BIGGEST impact he could have is in a situation where the bases are loaded. You have to go with the opportunity you have.
2. Why wait? Why does it matter if it's only the 7th? You have an opportunity to close the gap, tie it, or even take the lead. You might not have that opportunity later. It doesn't matter when you take the lead, a run is run! Why can't people understand this!
So lets recap: you have the biggest potential impact situation (Bases loaded, no outs) and you decided NOT to go to your best hitter on the bench so that you can reserve him for later when he might not have a chance to make a big impact (Ie, bases empty w/ a 2 run deficit). It's just not smart.
Finally, lets address the "But what about the 9th inning, 2 down situation". The best way to avoid that situation is to do exactly the opposite of what you are defending. Putting Papi in that spot (7th, no outs, down a few runs, bases loaded) will, in the long run, give you the most runs, thus minimizing the need to make a big 9th inning comeback.