[Nyororin]

Radiation sickness cannot be spread. Radiation contamination, however, can. If there is radioactive material on the body or clothing, it can be passed on to another person. The contaminated material may not be causing harm to the contaminated individual, but it has the potential to be ingested/inhaled and cause harm to others.

This is why hospitals are asking those who are coming from contaminated areas to be properly decontaminated. Most hospitals don`t have the facilities to decontaminate patients, so they are asking them to go to decontamination centers (mostly set up at shelters) so that there is no risk to the doctors or other patients. (In response to the other thread about being "turned away" because of radiation.)