Question about something in the plot...

When Waters frames CJ, he says a white MP had been shot, and that two other black soldiers had been shot, too. He set it up to look as though CJ had done the shooting. Now, here's my understanding of the chain of events:

1: White MP is shot
2: Black soldiers are shot in reprisal
3: The men hear the shooting and begin to wake up
4: The lights come on and Waters and Wilkie enter the barrakcs with an MP
5: Waters demands a search and then finds the planted gun

Now, where in this did Wilkie plant the gun? The men woke up right after the shooting; they were up and moving as soon as shots were heard, and the lights came on immediately after...I bet no more than 3 or 4 seconds passed from the time of the last shot to the time Waters came in. So, the gun had to be planted before the shooting, implying that Waters is the one who shot the MP...otherwise, how could he possibly know what was going to happen, and plant the gun? Wilkie later confirmed that Waters planted the gun in an attempt to scare CJ. So, here's my question; did Waters murder an MP just to get CJ in jail? It's not out of line with his behavior, but they never expressly address this question and I wondered about it. I figure he had to have done it, which makes him even more disturbed than I thought.

Opinions?