The US Environmental Protection Agency is clearly more concerned with ingestion than direct exposure: see http://www.epa.gov/radiation/understand/pathways.html
Skin will actually block most of the alphas and the neutrons. X-ray and gamma rays of course would go through the skin.
Remember, the radiation travels in straight lines from the source and is typically absorbed when it impacts a solid enough target. It affects the area around the source. Radioactive particles themselves create radiation. So the propagation of radioactive particles by wind or other vectors is the primary method that the danger of radioactive exposure can spread from the immediate area around the source.
If someone ingests radioactive particles either through air, food, or water, it will continue to irradiate their body from the inside as the material decays. This is clearly worse than a temporary exposure.
If someone is exposed to a source of rays but not radioactive particles, typically their skin and clothing will provide protection from some kinds of rays, but not all. When they are removed from the source of the rays, there is typically no residual radiation.
It is worthwhile to realize that there is a background radiation from outer space that is not absorbed by the atmosphere. Therefore, unless you live in a lead lined bunker or under the ocean you can not completely eliminate exposure to radiation. Levels of radiation comparable to this background level are considered acceptable.