It's been mentioned on here by others before, but I seem to recall that Weis's original choice for Defensive Coordinator had to back out due to health problems. Minter was then brought on-board as a last minute replacement since he has head-coaching experience and has been at Notre Dame in the past, both of which Charlie Weis saw as plusses. Many of his assistants have been head coaches in their own right at other schools, and Charlie wanted to surround himself with people who would be willing and able to question the way he was running the team.
But that's important and interesting to note: Rick Minter was NOT Charlie Weis's first choice.
You may be partly right. They are correct that Cutcliffe had to resign as QB Coach due to a heart attack offseason. (That put in a crimp in Weis time management as he had expected Cut to tutor Quinn allowing CW to focus on overseeing all aspects of the team. Cutcliffe was expected to return but had complications so ND asked the NCAA for a waiver to allow Ron Powlus to be a temporary onfield coach until a replacement QB Coach was hired. Weis ended up spending a lot more time with Quinn than was originally planned.)
BUT (here's the part where you're right, Vince) if I recall correctly CW originally wanted Al Golden who was the DC at UVA. Golden was reported to have said, "Yes!" but then decided to stay at UVA reportedly after a substantial counteroffer was made. In addition to being DC, Golden was also a highly regarded recruiter. Twelve months later Golden left UVA to become Head Coach at Temple.
I believe CW then approached Minter who had become the DC for Lou Holtz at SCAR in'04 after he was terminated by Cincinnati as Head Coach. Holtz subsequently retired and Spurrier had just become HC retaining Minter as DC when CW called.
Polian wasn't first choice at Special Teams either. Richard Bisaccia was reported on the internet but if I recall correctly there was a conflict of some sort (contractural??) and he bowed out.
