The President is the Commander in Chief - he could override all those decisions on who to promote, theoretically. At least that's how I understand it.
If they have a smart group that is actually planning this, that group could then vet a bunch of other people that their data suggests would be more amenable to their agenda and present a list of alternate promotions to the Republican president, which he could then order the military to make happen.
You know, this explanation makes it make sense to me a lot more than most of the others I've ever gotten.