I looked at a few historical math ratings and most have Michigan #4 for that year. Behind not only us but also UF and Tennessee. Sagarin says we would have won by 15 on a neutral field vs Michigan that year.
One reason for the ridiculous split seems to be that Michigan beat a lot of teams who were overrated at the time they played them. In their season opener, they beat #7 Colorado, which seemed a lot less impressive by the time CU finished 5-6. In game 2, they beat a ranked Notre Dame team by 7 points, but ND went on to go 5-7. Michigan's big win where they rose to no.1 was when they beat undefeated Penn State 34-8. That is definitely not a bad result but seemed a lot less impressive when PSU finished the year by losing to Michigan State by 38 and Florida by 15. Michigan also beat then no.4 Ohio State by 6, but OSU proved itself overrated when they got blown out in their bowl. Poll voters usually seem to take into account how highly regarded a team was when you played them and don't seem to check later on if that opponent proved themselves to be overrated.
In the Rose Bowl, Michigan faced a WSU team that was more on par with a typical Holiday Bowl team and won by 5. WSU was cheated by the officials out of having one more play from the Michigan 15 or 20 yard line. Meanwhile, we beat a far better Tennessee team by 25.