That's probably part of it. Plus, Ivory had complained a bit to the media, and even made a few trade noises. The Saints may not have wanted to give him too much of the spotlight after that.
If Ivory is not practiced at interviewing, he may have stumbled with the intense questioning... Questions not about the game, but questions about his playing time, trade value etc. The stuff that some of the dirty media types want to hear..
Also, imagine, if you were shy about having to give pressers.. especially after you do good or bad in a game.... and then imagine... if coach told you before the game, not to worry about having to give a speech afterwards...just play the game...
Not to say he is a Rickey Williams sort, I don't know him at all, but some people get really bothered about public speaking.