Before you pursue this further, ask someone who's spent hours sitting in one of the nylon seats on a C-130. Decidedly uncomfortable. Go for a C-5 or C-17 instead.
C-5 will just end up broken down on the runway for days. Take the C-17.
Perhaps they mean commerical C-130s because military C-130s (or any other kind of cargo aircraft) are not available to members of the general public.
http://en.wikipedia.org/wiki/Space-A_travel
Also, I took a trip once in a (military) C-130H. Very loud (we had earplugs though), nylon mesh seating, but I was comfy and I slept or read most of the trip.
Can you elaborate on that at all? The link you posted doesn't mention military hitchhiking, which sounds interesting to say the least.