I somewhat disagree with that. Time of possession is important depending on the type of team you are. With Nebraska for years it was important. For Oregon for years it wasn’t. Both were good teams.
I disagree in that TOP was "important for Nebraska" in their peak years, and Osborne wasn't necessarily trying to win the TOP. I think that's your perception bias. In NU's peak, Osborne was always looking for a high scoring offense, and then the defense improved as the 90s went on, resulting shorter opponent drives and the ball going back to NU's offense. As NU got better, that resulted in more TOP for NU. In reviewing 1990-1997 (peak Osborne years), let's look at how much TOP advantage NU actually had in those seasons.
1990: 29:35 NU, 30:25 opposition - this was a great NU team, led by Mickey Joseph, until the last month of the season, when it lost to Colorado, Oklahoma, and Georgia Tech
1991: 29:23 NU, 30:37 opposition - this was Osborne's first Big 8 title team in since 1988
1992: 31:12 NU, 28:48 opposition - Frazier's first year as starting QB, and that wasn't until midway through the season
1993: 31 NU, 29 opposition - undefeated regular season, lost to FSU in NC game
1994: 33:35 NU, 26:25 opposition - biggest TOP advantage by a NU team, but this team had issues at QB after Frazier's injury and lost a lot of big play ability. This is the one season where Osborne focused on shortening games and relying on the defense
1995: 31:56 NU, 28:03 opposition - much shorter TOP advantage than previous year, as NU was able to rely on more big plays on offense, also had an amazing D
1996: 31:11 NU, 28:49 opposition - first year starting QB, not as strong as offense as 1995, also had injury issues at I-back
1997: 32:48 NU, 27:12 opposition - 2nd largest TOP advantage of Osborne's 90s teams.
Looking at these numbers, other than 1994 and 1997, NU didn't have huge TOP advantages over their opponent. My argument about TOP not being a strategy by Osborne's teams are:
1) TOP can be skewed by slowing tempo and limiting possessions -- Osborne wasn't doing this. Osborne wouldn't want to limit possessions, as he had better talent than most teams. Osborne would want NU to have more possessions during a game, and more opportunities to score.
2) Osborne's offenses did skew the TOP more towards NU, mainly because it moved the ball primarily by running the ball, thus keeping the clock running. If a running team has an unsuccessful play, the clock still runs. If a passing team has an unsuccessful play (incomplete pass) the clock stops.
3) TOP can be skewed by teams with the lead trying to "run out the clock" when the game is in-hand. This was a common occurrence for peak NU teams.
Time of possession advantage can be a by-product of successful and winning teams. Time of possession advantage can also be a by-product of less talented teams trying to limit possessions and scoring. That's why TOP isn't a good indicator of winning a football game.