I do not see how whether or not Burke or someone he spoke to above that, perhaps putting pressure on the USCM to not take the mission seriously, makes him any more manipulative than already implied.
If he did I do not see the potential to throw Gorman under the bus anyway, because Gorman's likely as much in the dark as the rest of the Marines, and the Bishop android as USCM property also.
In fact I find the idea Burke spoke to someone above him, and that person arranged things so whilst not directly interfering, and risking putting their name on trial they did make it more likely Burke might have the final say through simple deference fairly plausible.