Here are some numbers. Keep in mind for the brevity of the discussion, I just included all games from 2011-2012 as during Sutter (except for Carter, since he was in Columbus until the deadline and it is easier to track), which is skewed by the fact the Kings played under Terry Murray until December:
Kopitar's PPG before Sutter: .91
Kopitar's PPG during Sutter: .85
Carter's PPG before Sutter: .73
Carter's PPG during Sutter: .75
Brown's PPG before Sutter: .59
Brown's PPG during Sutter: .45
Brown clearly had the biggest dropoff. But you can see Kopitar's average production remained the same while under Sutter, while Carter's actually improved under Sutter.
Team performance
GF/G in 2012 playoffs: 2.85 (3rd in league)
GF/G in 2013 regular season: 2.73 (10th in league)
GF/G in 2013 playoffs: 2.06 (11th in league)
GF/G in 2014 regular season: 2.41 (26th in league)
GF/G in 2014 playoffs: 3.38 (1st in league)
GF/G in 2015 regular season: 2.66 (18th)
GF/G in 2016 regular season: 2.72 (14th)
GF/G in 2016 playoffs: 2.20 (13th)
GF/G in 2017 regular season: 2.43 (24th)
So, the Kings had a couple down years, but they also had a couple years where they were middle in the pack in terms of offensive production. They also typically amp up their performance where they are a top offensive team in the playoffs.
Ultimately, it becomes a war of attrition for Sutter's players. They play a heavy style that wears down the opposition, but it in turn wears down the Kings players as well, playing it over the course of an 82 game season + playoffs.
So a team like Winnipeg would greatly benefit from having Sutter's direction and discipline, but like the Kings, they better win something in a 3-4 year window.
Your "fact" is just an opinion, although I'm interested in seeing your evidence to support your claim that all offense dies with Sutter and players would have their offense stifled and imploded.