They don't have to penetrate the skin to cause extreme harm. The problem is that radioactive material becomes diffuse in the environment and is ingested with food or breathed in.
I don't know who told you that radioactive substances were safe but they lied to you bro
LOL
At first I thought you might be an incurious highschool teacher or general practitioner parroting from an induction briefing.
Now I realise, you got nothin'!
If a large number of atoms of radioactive material are ingested (which can present as a single speck, which adheres together and travels together to some resting place in bodily tissues), then the repeated decays from adjacent atoms (as well as further decays from the decay chain) can overwhelm the recovery mechanisms of the tissue right there which keeps getting hit over and over by ionizing alpha particles. This is totally true, and this is why nuclear fallout is so dangerous for about 2 weeks after a nuclear explosion.
But:
1) If you dilute material properly, there will not be clumps of radioactive atoms. The atoms will be mixed with non-radioactive atoms. So my argument is that if you properly dilute radioactive waste, there is no appreciable danger anymore.
2) Fallout after a nuclear explosion, after about 2 weeks, isn't going to kill you anymore. Even though the nuclear material may be clumpy, the hot stuff has decayed far enough.
The #1 risk of being near a nuclear explosion is the thermal flash, which kills at the greatest radius. But you should also avoid fallout for two weeks. Two weeks is approximate, there is a 7-10 rule that says for every 7-fold increase in time there is a 10-fold decrease in radiation.
