No, they didn't.
But there's a lot we don't know about that exchange. For example, we don't know the specific line of questioning that caused him to go off.
Think about it for a moment. If a reporter calls Pat and says, "We're planning on running a story about the lawsuit filed several months ago concerning the softball coach and allegations of player abuse, do you have any comment?", why would that trigger Pat into a "profanity-laced tirade"?
I think there's a better chance that they asked him about something else. Something that isn't explicitly mentioned in the article.
As for firing him vs. ginning up some kind of controversy, that's an easy one. It plays into the larger strategy.
Brown is on the BoG. The expectation is that Amy Towers will also be on the BoG. The plan is to spin up an independent entity to have oversight with regard to athletics, similar to that at other competitive schools - see the University of Florida's "University Athletics Association". This entity would have complete control over all aspects of the athletic program, with a dotted line to the BoG, but would be independent of the Office of the President.
Another athletics controversy at RU sharpens the narrative into something like, "There have been too many problems under the current operating model and, with Big 10 membership, athletics is too important to be managed in the traditional mode, going forward."