http://data.un.org/CountryProfile.aspx?crName=Yemen gives a gross income per capita for Yemen of around $1300. http://en.m.wikipedia.org/wiki/Economy_of_Yemen has a more optimistic $2200. Sana'a may be richer, but I guess the poor will be significantly below that.
I don't find it strange that they will not be able to pay for the infrastructure and the additional costs of desalination and of pumping the water to the city (over 2 km up)
Also, looking at http://files.transparency.org/content/download/700/3007/file..., Yemen is perceived to be extremely corrupt. That means that its population may not trust their government with that amount of money, even if they could afford to pay it.
http://en.wikipedia.org/wiki/New_York_City_Water_Tunnel_No._...
50 years and $6 billion for a tunnel 60 miles long. The city owns lots of land around the source waters, but I think that is their only expense in acquiring the water, and the tunnel flows downhill to the city.
Also, the 21st President of the United States was Chester A. Arthur.
Not everything has to be a Fermi thought experiment.
It's not the OPs inability to believe that's the problem. Show him all of his flawed assumption and he'd readily change his mind (I would hope anyhow). But how do you disabuse him of those things which he takes for granted here in the US? That's a difficult process.
But if this place is indeed the equivalent to Manhattan I can understand the disbelief. Compared to the trillions tied up in real estate the cost of a pipeline to NYC would be trivial. Yeah it might cost $50b (probably much, much less but lets go crazy) but with at least 10mm people around to receive the water it's $5k per person amortized over a decade it comes out to $50/mo/person
I realize that the economics in Sana'a are probably hugely different than here in the US. But if people earn less, labor is cheaper too, etc.
The difficulty here isn't that given the facts it could happen. It's that getting to the point where you have all the facts has turned all the assumptions that you normally take for granted completely upside down. Speaking as an engineer I can understand the difficulty.