I think that map is really showing the AT&T Long Lines network, which carried all networks, not just NBC. AT&T's Long Lines division really was synonymous with long distance. The local Bells routed a long distance call to Long Lines, who was responsible for the major city connections. They also handled all network TV, radio, some telegraph, wire photo services, etc.

Here's a link to a 1952 Long Lines map that if you follow the legend for the coaxial cable you'll see that it's basically the same map: http://www.long-lines.net/places-routes/maps/US52.html

Here's a link from the same website for a 1947 Radio News article about how networks were going to get their programs to local stations and about the coaxial cable. Note that the opposite of what the article predicted came true. AT&T ended up routing tv over coaxial cable and phone calls over microwave instead of the other way around: http://www.long-lines.net/documents/...7/f-cover.html

Finally, from the same website, here's a picture of the Kansas City AT&T facility network tv board in 1966. This is where they fed the network feeds to local stations and passed them further along the chain to other cities.