Comment by ModernMech

> (in certain narrow cases)

Again, citation needed. The whole problem today is that the category of immunity is so vague so as to be overly broad.

> It does not say that members of the military have immunity for following an unlawful order.

No, but it does say the President has an unreviewable pardon power to absolve them from any crime they are ordered by the President to commit.

> It would also be very easy for a court to decide that executing a political rival is not an official act and deny the President immunity.

It's now also very easy for a court to decide that it is. That is the problem.