There should be no question that DU can be hazardous under some circumstances, but referring to it as "radioactive fallout" or "radioactive waste" is rather excessive. The US Department of Veterans Affairs has been studying it for a number of years and has this to say about it:

DU is natural uranium left over after most of the U-235 isotope has been removed, such as that used as fuel in nuclear power plants. DU possesses about 60 percent of the radioactivity of natural uranium and is a radiation hazard primarily if internalized, such as in shrapnel, contaminated wounds, and inhalation. In addition to its radioactivity, DU has some chemical toxicity related to being a heavy metal (similar to lead).