Their hypothesis is that the centrifugal forces would have concentrated heavy elements like thorium and uranium on the equatorial plane and at the Earth core-mantle boundary. If the concentrations of these radioactive elements were high enough, this could have led to a nuclear chain reaction that became supercritical, causing a nuclear explosion.
Granted I do not have their entire hypothesis here but I do see a rather obvious contradiction here.
First they say that isotope ratios of the Earth and moon are nearly identical. Next they follow with the hypothesis that the Earth spinning fast enough to concentrate heavy elements at the equator and a following explosion ejects enough material to form the moon.
If the material ejected to form the moon happened at the proposed time the moon should be either composed of a higher concentration of heavy elements than the Earth or a lower concentration of heavy elements than the Earth.
My guess is that the moon should have a high concentration of heavy elements because the higher concentration of heavy elements at the equator would be the most likely to be ejected because of their greater tangential velocity. .
The other issue I have with this hypothesis is that super critical reactors do not explode unless contained in a pressure vessel. They melt. The only possibility of an uncontained reactor exploding is if some material contained by the reactor reached its flash point. But generally an uncontained reactor reaching super criticality would simply melt and due to its decreased density would simply fall below criticality and shut down.
Right,they're going to have to come up with more evidence to convince me, but... interesting theory.