The Chunnel also cost about $17 billion in today's dollars and is only 31 miles long (including the above-ground parts). I don't think this is a feasible model for long-distance transit, especially when Musk claimed a cost of $6 billion for SF to LA.
With SpaceX Elon has demonstrated an ability to reduce costs by a factor of 10 in large part by eliminating the use of contractors. If you look on the PandoDaily interview, just before the Hyperloop is discussed he was railing on about how inefficient the 405 highway expansion is. I wouldn't be surprised if he thinks that he could save an even bigger factor in that kind of public work than he did with SpaceX.
I'm not saying that he's right. I'm saying that his cost projections are extremely unlikely to start with existing construction projects as a base line.
http://en.wikipedia.org/wiki/Hindenburg_disaster
A tunnel filled with hydrogen has a large surface area for potential leaks.
Suffice it to say, the challenges of an electrically grounded hydrogen tunnel lined with heavyweight materials using modern technologies & sensors are a hell of a lot different than the challenges of an ultra-lightweight, ultra-thin flammable gas bag before the advent of plastics, in an electrical storm.
A tunnel filled with vacuum has it a hundred times worse, because you're dealing with 15PSI trying to get in rather than 0PSI pressure difference diffusing out. We already regularly use larger-molecule methane at thousands of PSI.
Obviously a modern hydrogen tunnel would be much different than a zeppelin, and have different challenges. Still, 400 miles of 10-foot diameter tunnel would have plenty of opportunities for problems (whether it's evacuated or filled with hydrogen or something else). I'm not sure an evacuated tunnel is necessarily worse from a safety standpoint, though. It might be harder to engineer, but the failure mode seems safer. A hydrogen tunnel means that a leak will mix hydrogen with an oxidizer. If it's at 0 PSI, this could mean a leak lets oxygen into the tunnel (either due to high-pressure weather or due to hydrogen rising from the leak, leaving a low-pressure environment in the tunnel). If you wanted to fill a tunnel with hydrogen, I think it would be wise to keep at least a small positive pressure to ensure than any leaks are outward only.
I'm totally unclear why methane stored at thousands of PSI is relevant. Is there some 400-mile long, 10-foot diameter, above-ground methane tunnel I'm not aware of?
There are already some very long vehicular tunnels at depth (the Chunnel, Seikan Tunnel, etc.). I don't think one atmosphere more or less would be a showstopper.