Did Barnes kill Manny in some sick plot to harden his men?

Did Barnes kill Manny in some sick plot to harden his men? My mom had explained to me that, to her, when Chris' and Barnes' eyes meet slightly before they notice Manny is missing, Chris had caught Barnes reflecting on killing Manny (Chris doesn't know this, he is just watching him because he looks troubled, part of why Barnes is startled when he catches Chris looking at him. She says he had just killed Manny before getting back to camp and was settling in when Chris starting to watch him). They notice Manny is missing when they go to move on from that point. Then they find Manny after this, mutilated. She says it was Barnes. HE is the psychopath killer in this movie. He hates the enemy. He kills Manny in order to stir up the men and make them more ruthless. He wants to make them into killers like him. He wants to make them hate the enemy like he does. After he kills Manny and gives them the speech, many of them are ripe to "do the whole town". They don't question his tactics. He definitely goes over the top at this point. Killing the woman, and such. I had always thought this to be so. Everyone I tell this to thinks I am crazy. I just took my mother for her word.