Actually he was the wrong person to deliver the message. Since his job was on the line too, bonehead prolly thought he should stick around and see if allegri gets canned so he could stay.
Better that he gets involved in a media tit-for-tat with a guy who is owning himself with his contrary remarks? Like he said, he's said his bit already so Bonucci can continue to punch himself out and look like a clown, which seems his intent.