I've hear Deion (of all people) say this on NFL network - if you need motivation to play you shouldn't be playing. He was calling out the bulletin board material myth. I think it was about Kitchens t-shirt.
It's like some kind of old wives tale left over from the Rudy movie or the endless Marty Shottneheimer speeches on NFL films.
What exactly do you expect a head coach to do as far as motivation? Yell at them. Break a bat over his shin. Worked well for Singletary didn't it? Yelling at his team and exposing himself to them.
You think Bellicheck motivates his players? How about Pete Carrol?
Players respond to a scheme they believe in, an organized staff that doesn't make them do stupid stuff for no reason and fear of being replaced. That's probably about it.