There's really no problem. Mark Anderson had 12 sacks despite only playing 28% of the defensive snaps last season, and we drafted Dan Bazuin in the 2nd round. We have depth and I think Brown knows that a) either he's soon going to be gone anyway, so he might as well look out for his interests; or b) due to the depth, he'll have little positioning power when trying to redo his contract which he says he wants to do.
He also said in the interview that the Bears have no plan to trade him, he's just looking out for his interests.