The responsibility for the diminishing of Mike Tomlin's authority may not totally rest with Art Rooney II. Tomlin must've understood that the Steelers ownership was unhappy with the offense: they indicated that at the end of last year and again at the beginning of the 2011 season. The $64 question is: did Mike Tomlin have any dialogue with the ownership about retaining Bruce Arians prior to his premature statements that Arians would be back. If not, then it was he, rather than an Art Rooney II, who caused the awkward release of Arians as coordinator. If Tomlin had any inkling that the ownership wanted to replace Arians, he should have been mute on the subject. If Tomlin had no such inkling, then he's not as perceptive as he appears to be. All of this of course is speculation and conjecture; none of us really know what actually transpired. There's no question that the release of Arians was not effected in the usual Steeler way. In my view, Tomlin is likely not lily white in the matter.
One thing I do know is that upper management always retains the right to change personnel. Sometimes the persons directly responsible for the personnel involved cannot, for whatever reason, bring themselves to make the changes that may be required.