I think what the article argues is exactly this: there would be less hyper-connected nodes if the nodes would be more locally connected. The spreading of the disease would happen much more slowly in this case. This fits in with the theory of scale-free networks.
links:
http://en.wikipedia.org/wiki/Small-world_networks
http://en.wikipedia.org/wiki/Degrees_of_separation
http://en.wikipedia.org/wiki/Watts_and_Strogatz_model
http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_m...