I am not sure, isn't the Head Coach ultimately responsible for knowing and then approving recruits as players onto the team?
It's quite simple.
Players on the current roster do not have character issues. They're all best friends and it's only a matter of time before they jell into the national title contenders they're destined to become.
However, if a player transfers, then he definitely maybe had some kind of issue with their character or their camp that simply could not be foreseen. You can't blame a coach for the behavior of a bunch of immature teenagers and twenty-somethings. Good riddance. We're better off without him.
If a player has character issues as an underclassmen but then matures during his time with the Illini, you can credit the coach for developing him into an upstanding young man.
And if a coach stops recruiting a highly sought-after player, it's probably because that player had some sort of character issue. In this case, it was probably a chronic, uncorrectable malady and the coach is to be lauded for prioritizing his locker room over stars (btw stars and rankings don't matter unless we get a commit from a player with a high ranking or a bunch of stars...but that's a different conversation).
Hope that clears it up for you.
Ps. You can be forgiven for not knowing these basic principles. I used to think coaches did their best to balance character with performance but that predicting the behavior and attitudes of young men is an imperfect science. You just have to hope you win more than you lose, but the coach ultimately gets credit for both the wins and the losses. That's what I used to think anyway.