First of all, there is no rule that says that an NCAA waiver could be granted just based on the departing school (Illinois in this case) not objecting to a transfer playing immediately. The one year sit-out transfer rule has nothing to do with the departing school objecting or not objecting to waiving such year. The departing school has no jurisdiction deciding on whether the transfer can play immediately.
Furthermore, there is absolutely no way that any AD, or any University will admit to a coach "abusing" s student-athlete without taking action against the coach. That would amount to self-admission of guilt and a cover-up, in exchange for supporting a recruit's petition for another school. The legal and financial exposure of such action would be huge, really devastating. Not only would the coach be destroyed, but the AD as well, and the University could face huge negative PR, legal, and financial exposure.
A departing school can help a transfer's petition of a waiver if that waiver is based on medical/psychological evidence by further providing evidence in support of the player's petition. That could obviously happen if the waiver is based on medical/psychological reasons. But a University would never concur to self-incriminating abuse allegations.