I believe that 18 U.S.C. § 1385 specifically bans the US military from acting on US soil, full stop. And, while we are currently in permanent war post 9-11, in general the President needs to wait on an act of Congress to engage in deploying the military. I'm by no means a lawyer, much less a legal or constitutional scholar, but I think my question stands, maybe better written as:

Given that such acts are banned by law, (deployment of troops on US soil, for instance), how would a President who wanted to assassinate his rival be able to claim this occurred within his official capacity?

I would generally agree with the court that putting justices in charge of weighing Presidential motives isn't really a world we've had or would want. But others of course might disagree.