There is a tendency-- not limited to this board-- to take the idea that defense wins championships or high powered offenses don't and turn that into a mantra or caricature of sorts.
Certainly one dominant aspect (offense or defense) can make you a contender. But if the other side of the ball isn't that effective, your chances of winning it all are decreased. Saying it's necessary to be balanced, though, is just another over-generalization. Still, I think there is some truth to striving for balance (being really good on both sides of the ball). Certainly, LSU's 2011 offense (for whatever reason the offense became progressively worse with the switch to JJ after the first Bama game) is what kept it from winning it all (in contrast to Bama's better balance on both sides of the ball that year.
In the last 20 or so years, off the top of my head , UF in 1996, Texas in 2005 and Auburn in 2010 were championship teams that were more highly regarded for offense than defense.
In my mind the next group of teams I mention is debatable, as these teams all had highly regarded defenses. But Urban Meyer's at the time innovative spread offenses which won the BCS for UF in 2006 & 2008 could put up a lot of points; so could the USC teams of 2003 - 2004 (despite one being AP only and the other being vacated due to infractions). I don't remember clearly, but suspect FSU in 1999 and Miami in 2001 were pretty high scoring. And the Nebraska teams of the mid 90s might not have had much of a passing attack, but had very high powered running games.
I think the only thing that can be said with certainty is that if a team has a high scoring offense, but average or worse defense (like Mike Leach's Texas Tech teams... and arguably Oregon the past few years... though Oregon's defense started to be competitive) you will have trouble winning it all. But even those TTU and Oregon teams have been very close to making it to the big game. And if they had made it-- who knows-- they might have been on that night the way Utah was when they made Alabama look silly in the 2009 Sugar Bowl.
eta: I was assuming football, too. But the general premise of being really good on both offense and defense (not necessarily fantastic on one) has merit for any sport.
This post was edited on 5/13 at 12:06 pm