The real point, Foolestroupe is found in:

When hit by a neutron, it becomes uranium-239 (U-239),

Except in a nuclear reactor, or in the presence of rather high concentrations of U235, there are virtually no neutrons with sufficient engergy to produce the transition of U238 to U239 in significant amounts.

By separating the U238 from the other more energetic isotopes, the U238 by itself is rendered relatively inert. The extremely long half life means that spontaneous ejection of neutrons happens infrequently, and unless a very large mass of U238 is concentrated in a small area, most of the ejected particles simply don't hit anything.

Perfect separation of U238 and U235 is impossible, but as your article points out it's necessary to get approximately 20% U235 to even be useful as a nuclear generator fuel. The 80% U238 that remains in the fuel can be converted by the neutrons emitted by the U235 into plutonium, which of course is an ideal nuclear weapons material. This is what's meant by a breeder reactor/reaction.

To make the 0.72% U235 in the natural (refined) uranium equal to 20% of the eventual fuel quality mixture, 97% of the U238 must be removed. The 97% that's removed is what's used for DU products. Without U235, or another equivalent energetic source of neutrons, the U235 alone won't produce plutonium, or even detectable radiation much different than the background levels found in many parts of the earth.

The Wiki article describes what happens to U238 in a reactor, but the DU is separated out before that happens, and is not exposed to the environment required to produce the other nasties.

Descriptions of what happens to carbon in a high neutron flux aren't much different than the Wiki description of the U238 to plutonium transition, but that doesn't necessarily mean that your granny's greasy skillet is "radioactive," just because carbon can be made to be.

John