You're saying that Tomlin doesn't pick his coaching staff? It's just a coincidence that Tomlin, Fichtner, and Butler were coaches at Arkansas together? I'd like to see a link to something that validates that Tomlin doesn't make those calls.
Butler has been here forever, definitely a Rooney guy. Fitcher may have been somewhat influenced by MT, but he was not put in a major position to begin with, but rather with influence from Ben, who likes him, to become OC. The Rooneys are not big fans of accountability when it comes to the decisions they make or influence. You're not going to find any link where this is stated matter-of-factly. But reading/listening to quotes, you can read the tea leaves.
For instance, if memory serves, MT gave Arians a ringing endorsement to return just days before Uncle Brucie "retired." (If you recall, the team came up with the "retirement" story which was never confirmed by BA. As a matter of fact, BA stated emphatically that he had no desire to retire at all, and never said anything of the sort whatsoever.)
Next we have LeBeau. Again, we were given lip service, as if MT was to make the call to keep him, by DL at least. MT made comments leaving us to believe DL would be back, but some mysterious force sent him packing (I am not complaining, it was time for DL to move on).
Next is Haley. I don't recall hearing anything about MT having meetings with him from what I recall. Haley's dad went way back to the Steelers and that appeared a Rooney call as well. Then, came more and more friction with Haley and Ben, to the point that Ben threatened retirement seemingly when it looked like DH would be back. After it was known he'd be gone, Ben completely stopped all retirement talk and began saying he had a good 5 years left. I don't see any evidence MT was in on hiring or firing TH. Again, not complaining, I wanted TH gone years ago.