Although I can't be bothered to read the PDF, I take it the good doctor hasn't heard of a little thing called ODX?
It's short for Olympic Dam eXpansion, a project by the world's largest mining company, BHP Billiton, to create the largest mine the world has ever seen. We're talking about an open cut mine that will eventually be over one kilometre deep and multiple kilometres in diameter where they'll be shifting more than one tonne of ore out of it every second, 24/7 for 100 years or more. They keep upgrading the reserve estimates because they haven't found the true extent of the ore deposit, which alone accounts for something like 30% of known reserves. Currently the mine produces around 5,000 tonnes each year, which isn't the largest (Ranger in the Northern Territory is) but if the expansion goes ahead on the scale they're planning then it will be spitting out much, much more.
Then there's some other large deposits in Western Australia that are only now being developed as a change of government has seen the ban on Uranium mining lifted. It's even worse in the eastern states of Australia, as they have prohibited even exploring for uranium. Hooray for the luddite Labor party! The party that is okay in South Australia and federally to be mining and exporting it, but not using it here and won't even entertain discussion of the pros and cons of Australia adopting nuclear energy.
So if there's a shortage then the price will rise (which it did in the last few years because of fears of running out of the cheap bombs) and that will spur miners to start mining already known deposits that couldn't be mined profitably at lower prices. It will also spur further exploration and eventually the price will rise high enough that it becomes more economical to reprocess spent fuel, which is apparently 90-95% still good.
There's enough Uranium out there that we'll never run out for centuries, and then there's Thorium if fusion continues to forever be 40 years away.