The Chargers only had a double-digit lead for less than 2 minutes late in the 2nd Quarter. Rivers attempted 32 passes and the Chargers backs combined for 29 rush attempts. Balanced attack it would appear.
Brady attempted 51 passes, and the Pats RB combined for 19 rush attempts.
IMO, what cost the Chargers the game was when Marlon McCree intercepted Brady, returned it 3 yards, and fumbled it back to the Pats. They then scored a TD five plays later and tacked on a 2-point conversion to tie the game at 21. If McCree had not fumbled the Chargers would likely have held on to win. They lost 24-21.
The Pats seemed to lead a charmed life sometimes. That game was one example. Another was vs KC several years ago, when the Chiefs were protecting a narrow lead and Brady threw an int, but Dee Ford of KC was very obviously lined up offsides. So the int was nullified and the Pats went on to score, and eventually won the game in OT. Ford had 13 sacks and 7 FF that season but KC traded him to SF for a 2nd round pick two months later.