the 'Cats reached #1. "Resurrection," which is a mediocre book overall, has an excellent account of what happened. According to the book, Parseghian said he'd finish out his contract in '63, and he would then be gone.
The book also recounts how Parseghian was changing planes to fly to Miami to interview for the 'Canes job when he checked w/ his wife to see whether ND had called. When she told him that ND had called, he flew back to Chicago.
Yes, dame fortune often plays a role, but, as B. Rickey used to say, luck is the residue of design.
EDIT: Dan Mullen, who has lifted MS St to levels I previously thought unattainable, was a GA @ ND. If I were JS, I'd have vetted Mullen by now, and I'd have an idea as to whether he might be a good fit and what his likely contractual demands might be. My guess is that JS has never even placed a courtesy call to Mullen's agent.