While strictly correct, this is extremely misleading. Current resources would be exhausted in a decade, but resources are defined as the known deposits extractable under current market prices. Should we actually start using a lot of uranium, the price would spike, which would lead to a lot more deposits becoming economically available. This has almost no effect on the cost of nuclear power, as the cost of the raw uranium isn't a large part of the cost of producing power.
The end game there is when the price rises sufficiently for extraction from seawater becoming profitable. The world's seas have ~1000 times more uranium than conventional ground-based resources.
Nuclear fuels will not run out in this millennium.