UNI was D2 until the early 80s so this can't be true.
You are correct. My memory was off. I'm sure the scenario I was thinking of was ISU-UI ranked 1-2, and UNI ranked 1st in DII, which could have been for a more extended period of time, than like a one time occurrence, which is more consistent with my memory.
They became DI in 1981 and DII in 1963, when they competed in both tournaments.
Prior to that their record in DI was pretty good, including this stretch under McCuskey (who then left for UI):
1946 2nd place
1947 2nd place
1948 4th place
1949 2nd place
1950 1st place
1951 4th place
1952 2nd place
Without looking into all the detail, I wouldn't be surprised if their NCAA finishes on the whole were better than UI, at the time they became DII in 1963. If you click on 1953 - 1964 Coach Bill Koll you can see that they were pretty regularly about 10th or higher:
Wrestling History at the University of Northern Iowa | Rod Library
Since this is a message board, note that I did not say definitively, but rather that "I wouldn't be surprised."
Until relatively recently, very few teams could claim even a single DI national title.