Of course I wouldn't debate this as to Peyton Manning's ridiculous experience as a player, because duh..
But I believe the notion of the 'halftime adjustment' is more on the coach's end of things. ie, winding down the end of the 2nd quarter trying to summarize the things that have or haven't worked and taking a few minutes with the staff - while Peyton et al are peeing and having oranges - to drill down a few quick thoughts and tweaks to those things that aren't working or could work better. Then coming into the start of the 3rd quarter looking at opportunities to implement any fresh ideas into the mix as the game develops.
The idea of having a whole different philosophy or scheme from one half to the next is a mislabeled, if not completely overblown, suggestion. But taking a minute to stop, regroup, put heads together minus the in-game competition, and try and deliver a better plan of action is what good coaches should, and do, in every game week in and week out. The quick and convenient, and oft misunderstood, labeling of this concept as a simple 'halftime adjustment' is what's been watered down for criticism sake.