My guess is Doc knows that if this team is going anywhere in the playoffs, it is going to be because of the big 4. Currently, they are very much out of sync, and I think Doc feels that they need to get a rhythm going again.
I also do not think Rondo is that hurt. I think he is dealing with bumbs and bruises, just like everyone, but if it were anything that they could actually cure by sitting him, he would be sitting. They are trying to lower his minutes to get him fresher for the playoffs, but ultimately, he is likely just going to have to play through these bumps and bruises.
More than anything though, I just think Rondo's issues are mental, and I don't think sitting out will help them get over them. He needs to build his confidence back up, and the only way to do that is by playing.