Yes, you are correct.
Signed,
Mack Brown (1979-1981 Iowa State WR Coach/OC; 1985-1987 Tulane HC, 11-23 in his three years; 1988-1997 North Carolina HC, 2-20 in his first 2 years)
Pete Carroll (1978 Iowa State Secondary Coach under Earle Bruce)
Earle Bruce (1973-1978 Iowa State HC, 8-21 in his first 3 years)
Johnny Majors (1968-1972 Iowa State HC, 6-14 in his first 2 years)
Houston Nutt (1993-1996 Murray State HC, 9-13 in his first 2 years; 1997 Boise State HC, 4-7 in his first and only year)
Dennis Erickson (Head Coaching Resume is basically all over the landscape and he had rough starts in his first year at 3 of his 7 Head Coaching stops)
I'm not sure if you misunderstood the weasel, but he stated "when they fail at it". Mack Brown built a solid team at North Carolina. He didn't fail. He struggled early, but he stayed and made the program successful.
Pete Carroll's time at Iowa State wasn't as head coach, so not sure why you used that one??
Earl Bruce was successful at Iowa State, despite how he started. He stayed until he turned the program around, so that one isn't a fail.
Without going into further research, all of those guys had success during their first head coaching tour. Many of them may have struggled to start, but they all stayed and enjoyed success before moving on to better jobs.
In short, your analogies sucked.