Some people are emotional Libertarians before they are Constitutionalists. Many Libertarians have an anarchist streak that tempts them to oppose any national power at all, even to protect the country from invasion, which is the President's duty. Rand would throw out the Constitution with the bathwater.
I cant agree with your point on the constitution. I doubt he knows that much about what the founders meant when they wrote it.
The funny part is, that he is against any foreign military interventions, which I might agree with on some points, but he is against any defense/security against foreign invasions.
How the hell does that make any sense?