Offsides would only be called by the Linesman or Line Judge.  Personal Foul for a QB hit would be the Referee or the Umpire, so I figured I'd take a look at those officials

The linesman (Ed Marion)

was born in 1927, meaning he was 58 in 1985 - unlikely to have a 18 year old daughter starting at BYU at that time.

A little research into his obituary shows that his daughers were born in 1943 (Patricia), 1951 (Cathleen), 1953 (Elizabeth), 1959 (Cecilia) and Joanne Marion-Walton (1963)  Beyond that, he was heavily Roman Catholic, as was at least Elizabeth (the only one who I find an obit for).  Joanne would have been 22 in 1985 so a possibility, but nothing connects her to the LDS faith or BYU that I could find.

The line judge (Vern Marshall)

Harder to find info on him, but he was born in 1935 and the few articles I find about him mention only two sons.  No LDS or BYU connections that I could find.

The referee (Tom Dooley)

Born in 1934, had only one daughter (Nina), who is listed as being born in 1959, so would have been 26 at the time.  A bit older than the story implies, but maybe an outside chance?  Family all lived in North Carolina, so again, no connections to BYU or LDS faith.

The umpire (Dave Hamilton)

Born in 1933, but in Salt Lake City and then got his degree at the University of Utah, so we've got the LDS/Utah connection!  Also had 3 daughters - Gena (born 1956), Rene (born 1958/1959?) and Kip Lynn (unsure of her birthdate).  The ages seem a bit off, but with the Utah connections, this seems by far the most likely case.  Would seem a pretty easy matter for a reporter to track this down and figure out the details, but this gives me hope that the story might have legs