No, I'm not. The low number that gets thrown about is for commercially available deposits at the present market price. The price of the raw uranium is a very small portion of the price of running a nuclear plant -- it could increase by two orders of magnitude and not have a material impact on the plant bottom line. At that point, it would be economically feasible to extract it from seawater, where there is enough of it for effectively forever.
Extracting it from seawater is, however, not necessary. Even small increases in the market price make a lot of new deposits available -- uranium is quite abundant in earth's crust.
The reason uranium and nuclear fuel is so cheap is that it was consistently overproduced during the cold war. Before the 2007 speculative bubble there was effectively no new activity since the last government-funded uranium boom.
I think he meant in the other direction. There is enough uranium for 20,000 years of consumption if we stop throwing away most of and actually burn it fully.
Current designs only burn a few percent of it, then store the rest as waste.
Nuclear really should be considered renewable, the only reason it's not is politics.