White and Willingham knew each other for a while and White knew him because they were both in the PAC 10. TW dithered on the 1st approach. The job was never offered to him at that time. White had to move on knowing that he couldn't hire a coach who wasn't fully committed and went with O'Leary. TW regretted his initial dithering having been lobbied by family and friends that he should take the job. He didn't pass up the job the 2nd time.
I don't have a link because I know this due to who I knew at ND. Granted it is 2nd hand stuff but my connections at ND were pretty strong then. I only learned this after TW was fired because the person(s) who told me were p.o.ed at TW's disingenuous constant self - myth making which rivaled those of CW.