The two theories of a) getting Burke out of the house away from any cops questioning and b) keeping him close to ensure he doesn't talk about the crime - both a) and b) are plausible. However i think that of the two, theory b seems the most likely course the rams would have taken if Burke has been the perp.
If Burke had been the perp, the rams biggest problem amoung many would be of him talking to cops. The rams would have more control over this if they were with him to supervise that this didn't occur, if burke was taken away from them, the rams have lost control of the situation and are relying on a 9 year old boy to keep quiet.
My theory has allways been that the rams knew the cops would be finding JBRs body, and they didn't want burke to experience seeing his dead little sister bound and gagged.