Generally speaking, low-activity uranium/depleted is a low radiation risk, chemical risk is the greater of the risks.. even if burned, and inhaled, alpha radiation is not the bad actor, its the chemical compounds being absorbed into the body. Its more akin to heavy metal absorbtion, cadmium, lead, mercury, selenium, etc.. Your lungs and stomach are an easier avenue into the bloodstream than the skin. Once inside the body, your body may not have a means to expell them, and they substitute for similar compounds, messing up the internal chemical body workings..
All radiation is not the same, as PCs mentioned, alpha is absorbed/stopped quickly its low-energy relatively speaking.. Gamma, is an ionizing form, it travels through the body, damages tissues, and leads to broken DNA strands that could potentially repair in a manner that would become cancerous, etc..
Unfortunately, radiation is a complex issue that is not generally explained in great detail to the public.. so it makes it easy to make the blanket statement that "radiation is bad". As mentioned elsewhere, earlier in this thread, radiation is all around us, every x-ray causes a bump in your exposure. If you live in a brick home with ceramic tile you get an extra dose, if you travel more than once a year by airplane, you're getting extra doses because there is less atmosphere to protect you from harmful radiation, if you don't ventilate your crawlspace, you may have Radon and are getting extra doses. Background radiation levels are something your body is persistantly exposed to. There is a very quantitative element to the critical nature of exposure, exposure per se does not indicate damage. There is an intensity and activity level that determines severity.
Depleted uranium is an isotope, enriched uranium is another isotope. any given element that is radioactive can have several isotopes. Each isotope decomposes in its own activity cycle. Enriched uranium is much more active, and is only a small fraction of the uranium deposit, and is the most valuable component to the ore. The fission reaction they are trying to activate in nuclear reactors must obtain a "critical density" which means that the Uranium concentration has to be increased to the point that a self-sustaining nuclear reaction (chain reaction) can be generated. This is where'/when splitting the atom happens, and the alchemy of old occurs. We turn uranium into not-uranium.. it can be thorium, lead, or some other compounds based on how the split happens, but it no longer exists as the element it once was... This releases huge amounts of energy as the mass balance is violated and excess mass lost is converted into pure energy.
Its an amazing thing, and unfortunately, sometimes our reach exceeds our grasp... it is also a dangerous technology, rife with a myriad of risks. This is a very technical issue thats being fought/played out in a very political arena. When it comes to technical issues, and technical arguements, unfortunately the desire to win leads to making the arguements emotional, gut wrenching, or symbolic. 99% of the population does not have a grasp about the nuances mentioned above, they only know, from every movie and the recent tsunami in Japan that radiation is Evil... Unfortunately, the issue is not so simple and its not a cut-and-dried.
Every moment in my life I am exposed to radiation, the bones inside my own body were built upon and contain elements that irradiate my own body from within.. My wristwatch has tritium dials. Its the scale/magnitude/relative intensities/length of exposure.. these things are critical when it comes to radiation.
Those are the types of details that genuinely address the issue. Using the term "radioactive" in the discussion(referrring to videos, etc, not THIS discussion) is designed to create the knee-jerk recoil of fear and loathing, to gain public support and sway public opinion. If the radioactive toxicity is the lesser of the threats, and the chemical toxicity is the greater of the threats, then any argument that subordinated the chemical arguement for the radiation arguement is sensationalizing - maximizing effect. Because a chemical arguement must bring into play ALL chemical compounds.. again, narrowing the argument, the focus, is actually a disservice, because its to the exclusion of all potential harms that occured..