It wasn't just the Gerry Faust comparison; as I remember it was also pointed out that Bob Davie also proved to be a poor head coach and yet he was allowed to fill out the full term of his contract.
The real problem with the Willingham hire was that Kevin White did an absolutely terrible job of evaluating whether Willingham was a good fit at ND. The linked story says that Dave Duerson, a former ND and NFL great, was on the ND BOT at the time and advocated for the hiring of Willingham, so maybe White felt he was backed into a corner. Whatever the reason for his hire, I don't think Willingham ever bought into the ND culture, and I remember reports at the time were that Willingham's wife absolutely loathed living in South Bend. You know the saying: happy wife happy life. Well, the opposite is also true. And then Willingham turned out to be a poor recruiter and a mediocre game day coach. Not a recipe for success. Willingham's subsequent failures at UW confirmed that ND made the right decision in letting Willingham go.
I think it was the media, not Willingham, who stoked the racial bias narrative, though Willingham probably didn't do much to dispel that narrative.
Kevin White left behind a pretty forgettable legacy during his time as ND's AD: the Bob Davie and Ty WIllingham hires, the George O'Leary debacle, and the premature 10-year extension on Charlie Weis's contract. Ouch.