I watched that whole second video Pablo posted above since the boards are pretty boring this morning to get my entertainment (these boards are pretty boring right now). I don't know that this has any bearing since you can't take that interview in a vacuum, so this is just a hypothetical for the fun of it.
If Brad sticks by his words in that interview, I don't see how he could justify getting rid of Paulsen. To paraphrase, he makes a statement that as long as Paulsen sticks to the plan that Brad will have Paulsen's back. He even references building via the draft (4 year recruits) versus free agency (transfers). It seems to me that Paulsen has stuck to the plan. He has stuck to recruiting freshman, has run a clean program with no short cuts, so that would seem to mean Paulsen has a very long leash regarding the on court performance.