i definitely can't speak to the technical aspects, but i do think his statement makes some naive assumptions about the security of analog communication. humans have been espionage-ing analog communication for way longer than we have digital, and we're good at it.
for another thing, though, neither the intelligence community, nor any other organization as large as the dnc, can anymore operate using analog communication. there's just too much data, and a significant amount of that data can't very easily be communicated in writing.
if we're just talking about using analog messages to send the very most important messages, like cipher keys in your example, then what you're saying makes a ton of sense to me; but, my understanding is that the dnc hacks were allegedly done through phishing links/social engineering/whatever, and i dunno that couriers would solve that (except to the extent that a single courier isn't going to carry 30,000 emails, but then we're back to the practicality of it). i feel like the solution is better training for the humans using the computers, not getting rid of the computers, so to speak.
i'm also mildly skeptical that detecting a compromised courier network is easier than detecting as compromised digital network. not saying you're wrong, just that intuitively it's easy for me to imagine ways of compromising a person without leaving an identifiable trace or physical clue; i would think it's comparatively difficult to compromise a digital network without leaving a clue. the computer side of that is literally just speculation on my part, but i think you're underestimating how good people are at spying on people.