It's best to get the details from the article itself, but my recolection is that the author of the theory is aware of this objection and explains that because uranium only forms compounds with silicates in the presence of oxygen, and because the early earth possessed much less oxygen than today, that around 60% of uranium would not have combined with silicates to form less dense compounds and would in its much denser elemental form have sunk to the core.
--Percy