Scientific American is flat out wrong, compare[1]. (Someone who states that "a breeder creates more fuel than it consumes" has to be wrong about many things.) Common rocks contain about 13ppm uranium and thorium, which gives them a 50x higher energy density than coal[2]. We will never run out of rocks. As a bonus, if we actually "burn the rocks", we end up with a lot of sand to be spread on fields, which counters soil erosion, serves as fertilizer, and captures CO2 through accelerated weathering. In other words, solar power uses land, nuclear power restores land.
It's a misleading, but technically accurate marketing point for breeders. More specifically it's fissile material, which is converted from larger amounts of fertile material used in the reactor. There's no violation of conservation principles, just some fast talk. Read your own links - as at least the first mentions this.
The second link is junk. The average distribution of elements in the Earth's crust does not mean each every and every chunk of earth contains exactly that distribution. And while many types of rocks do contain trace amounts of uranium, it's nowhere near 13 ppm. Though so far as I can see even that site didn't state that.
> It's a misleading, but technically accurate marketing point for breeders
That's the point, it's not technically accurate. A breeder makes more fissile material than it consumes. Fissile material is the fuel in light water reactors, but breeders use a different, more abundant fuel. I know that, you know that, and we both know that we both know that. But inaccuracies like this lead to the likes of Helen Caldicott dismissing the whole technology with a sneer such as "a breeder that magically makes more fuel than it consumes".
> trace amounts of uranium, it's nowhere near 13 ppm
It's about 13ppm uranium and thorium, in fact about 10ppm thorium and 2-4ppm uranium. And while energyfromthorium doesn't state these numbers explicitly, it clearly uses them in the energy density calculations.
> does not mean each every and every chunk of earth contains exactly that distribution
So "burning the rocks" will never work, because there are a few rocks that don't burn? It works even better, because some rocks burn better, e.g. Conway Granites at 56ppm thorium.
[1] - http://www.nuclearfaq.ca/cnf_sectionG.htm#uranium_supply
[2] - http://energyfromthorium.com/cubic-meter/