I'm sure he would love to "tell his story". The problem is that once he tells his story, they still get to pin him down on questions and lay a perjury trap. So while it might give him some temporary emotional satisfaction, they'll still get the thin threads they need to have him charged by a friendly prosecutor.
The other thing is that even if the committee were to allow live cameras, there's nothing requiring the media to show all the testimony. CSpan probably would, but the rest of the media would pick and choose the clips they want to show, and could still paint a distorted picture.
My thoughts exactly.