Radioisotopic dating parent daughter
In short, the assumption that decay rates are immune to outside influences isn't as solid as it once appeared to be.
For instance, polonium radiohalos are sometimes associated with polonium bands generated by the polonium being transported by hydrothermal fluids along fractures.
These two independent and agreeing dating methods for of the age of two primary members of the solar system formed a strong case for the correctness of his answer within the scientific community.
This just goes to show that just because independent estimates of age seem to agree with each other doesn't mean that they're correct - despite the fact that this particular argument is the very same one used to support the validity of radiometric dating today.
Later, after radioactivity had been proven to be a significant source of the Earth's internal heat, he did privately admit that he might have been in error.
What is especially telling about this whole story is the conclusion of the absolute truth of the conclusion based on premises that are weak, or at least not adequately demonstrated.