Alpha radiation is easily shielded from external exposure, but for that exact reason it's also the most damaging; gamma radiation, for instance, will mostly pass right through you, while alphas will deposit all of their energy right into your cells. They're shielded by your dead skin, but if you ingest or inhale them, then there's no dead skin to protect you, and all that radiation goes straight into your cells.

In fact, according to the weighting system that converts joules of energy absorbed (Grays) to severity of radiation dose (Seiverts), a joule of alpha radiation is 20 times worse than a joule of X-rays, beta radiation, or gamma rays.

And it's ingestion or inhalation that we're worried about from environmental contamination; not that the environment itself would become so radioactive, Fallout-style, that you'd take rads just from standing around - but that radioactive dust from demolition might get into the air, or that contaminants might leak into the groundwater.