You are perfectly right. This series was a good opportunity to actually show people how radiation works. They did make a good step by step of how the disaster unfolded though, which is great. Just above I made the point that most people don't understand how radioactivity works and they will probably mostly pick up the details of the series that are added for dramatic effect since they're mixed with real events. TV series have a strong influence on people's beliefs. My comment wasn't too appreciated.
Being irradiated does not really make human tissue radioactive. You absorb the radiation particles, not the radioactive material emitting it. But ingesting, inhaling, or absorbing the material through the skin will not only kill the person (from the inside), it will also make the remains dangerous enough to not want them seeping into the ground. Now the tissue carries around the radiation source. [0]
To use the bullet analogy from the series, what I said above is akin to being shot with bullets or ingesting a gun that's still firing. The first case might kill you, the second case will definitely kill you but it won't really kill others unless they plan on ingesting you, firing-gun and all.
Being irradiated does not really make human tissue radioactive. You absorb the radiation particles, not the radioactive material emitting it. But ingesting, inhaling, or absorbing the material through the skin will not only kill the person (from the inside), it will also make the remains dangerous enough to not want them seeping into the ground. Now the tissue carries around the radiation source. [0]
To use the bullet analogy from the series, what I said above is akin to being shot with bullets or ingesting a gun that's still firing. The first case might kill you, the second case will definitely kill you but it won't really kill others unless they plan on ingesting you, firing-gun and all.
[0] https://en.wikipedia.org/wiki/Acute_radiation_syndrome