I don't know how much we'd learn from atomic decay, except perhaps the ability to date an object via radioisotopes with a touch. However, I would like to point out that we're still trying to full understand what the human body is capable of. Suspension of disbelief is not unfair.
I'd like to point out Achiem Liestner, lead optician for Project Avogadro.
The sphere he is holding is a prototype for a new kilogram. It's a nearly perfect sphere. So perfect that, were it blown up to the size of the earth, the errors in it would be less than 2.4m high. He's quite the insanely talented optician. He also has a super power:
In addition to precision instruments, Leistner uses his hands to feel for irregularities in the roundness of the sphere. The research team has called his extraordinary sense of touch "atomic feeling".
No one quite knows how he does it. Certainly its some tremendously powerful accumulation of information from his fingertips. Perhaps our bodies are capable of more than we think they are. If so, a plausible explanation for extraordinary capabilities might be "why not?" All that is left is to explain why scientists, with all their precision, failed to find a repeatable experiment to prove psychometry out.
One answer could be along the lines of "water memory." Water memory is a homeopathic theory that water retains a memory of everything it comes in contact with. Science has not found any reason to believe this is the case. Every proposed hypothesis that has come forth has either been falsified or found to be unfalisifiable (and thus not scientific). However, all it takes is one repeatable success. Maybe your particular psychometry is a variant of water memory which, in your story, proves to have a valid scientific founding.
If anything, a story which includes a sketch of what sort of hoops homeopathy would need to go through in order to be recognized scientifically would be quite the interesting story, and by doing it in fiction, you're even in a position to create fictitious experimental evidence in support of the findings (something real scientists can never do)