Well, if he was an all-pro at the time, then saying he was the lowest cog on the team wouldn't be accurate. Pat was an average to above average punter at the time. Grigson was jerk for saying those words, but not really for thinking them.
I understand how personalities fit into management of OTHERS. Myself, I work for a paycheck, not praise. So if said to me, I would take those comments as a sign I wasn't going to get paid or would be worried about my future employment, but personally they would mean very little. As you said, its cut-throat, a business; so to me the money is what matters, or the potential lack thereof, not the words.
But Pat's a comedian, a character, and artsy fartsy guy. Emotions and feelings probably are an issue more than if he was a cold-hearted analytical type. He probably holds a grudge for a long time too.