It's convoluted to be sure. This is what happens when the focus isn't on hiring the best person. Bond Shymansky should have been hired as the volleyball coach when Dingman was hired (his resume was just plain better). After more years of losing, Iowa was fortunate enough that Shymansky was an Iowa City native and still willing to take over the program.
And this particular issue with the assistant track coach position doesn't necessarily invalidate Griesbaum's lawsuit. Her contention is that Iowa treats male coaches differently than female coaches. Trying to look at it objectively, it will be an interesting case. Iowa has canned under-performing male coaches. Lickliter obviously. Dahm in baseball (although he was given 10 years). Steve Houghton was allowed to stay on and retire from tennis, when that program was rather bad for a while. On the women's side, Dingman was let go in volleyball (they were dreadful). I don't know the whole story about Gayle Blevins retiring, although there were rumblings she was encouraged to do so. Which never made sense to me, if true. She created the Iowa softball program from nothing. Griesbaum was successful at field hockey, although the highest part of the program came earlier in her tenure. Iowa let her go due to improper treatment of players. Griesbaum will likely argue that coaches like Fran have done worse with openly swearing at players during games, slamming chairs, getting tossed out of games (Wisconsin and UNI). And that none of her workouts have put players in the hospital (like football did with rhabdo). Difference in those cases is that none of the players went to the administration and complained about the coach.
A lot of waters for Barta to navigate in the coming months. New president may have different ideas. If the outcome of the Griesbaum suit goes against Iowa, I don't see how he would survive that. If football goes 6-6 or so, does he make a change there? There have been positive movement in many of the Olympic/non-revenue sports, he just should have taken action in those areas sooner. Baseball positioned much better. Volleyball much improved with a new coach (but the B1G is brutal). Men's and women's golf much better. Track much improved under guidance of Joey Woody. Women's soccer made title game of the B1G tournament last year.
But the lawsuit and the performance of the football team will likely determine his fate.