Incidentally, i think that you're proposing a test for susceptibility to the medicine. The relevant theory here is that any person who would be killed by a full dose, would be also be harmed but not killed, by a much smaller dose. That's a perfectly testable, falsifiable theory, but i don't think it would directly test the claim that the cause is genetic.

A better test for genetic causes, is to look at family relationships. If we believe the cause is genetic, then we predict that people who are more closely related to each other, are more likely to have the same reaction to the medicine. And we predict that identical twins would always have the exact same reaction to the medicine.

The original poster was looking for a very easy example that children could follow, without needing to understand any maths or probability theory, so I wanted to keep it simple. That's why i didn't mention the idea of improving the original scientist's theory.