If we observe only the statistics of radioactive decay, how do we know the physics that determines what nuclei disintegrate and which don't?
a) Pteridine, I strongly suspect that you've
already been exposed to explanations of the enormously-long list of things nuclear physicists know about nuclei, and how reliable those explanations are, at everything from the lowest energies (like, quantum-mechanical diffraction of millikelvin neutrons, which bounce off of a "neutron mirror" made out of the long-range neutron repulsion of nickel atoms? Our theories work just fine.) to the highest energies (Predict how pions diffract while exiting the fireball of a lead-lead nuclear collision at 200 GeV per nucleon? Our theories work just fine.) and in between (predict how often a neutrino-12C collision ejects one vs. two protons, and how that differs from neutrino-16O? Our theories work just fine.). I suspect you don't need to hear it because you already heard it and didn't care.
b) Boy, if there were a new nuclear-physics phenomenon in the world, and we were trying to judge
how badly it differed from current understanding---well, it'd be nice to try to learn about from someone
doing controlled experiments and obtaining nuclear data. Instead of someone whose "experiments" consist of a mixture of (admittedly, IIRC) lies and (allegedly) truths involving incompetently-instrumented black boxes.
c) Let's clarify
how far beyond reason Rossi's claims are. Every time the real physics world suggests something weird---dark energy! Higgs bosons! Dark matter! FTL neutrinos! The proton radius anomaly!---there is an vast army of amateur physicists who will spout
ideas for new laws of physics, or reinterpretations of known laws, to explain what's really happening.
Here's the thing, Pteridine. Rossi's claims are
so incoherent that not even the crackpots are interested in them. It's easy for you to say "wacky results can be true if some new physics is at work"
if you're not actually looking at the wacky results and understanding how wacky they are. In the almost thirty years (!) since Pons and Fleischmann, I can think of
only one crackpot even able to
suggest how "nuclear reactions might not release gammas" could possibly work. (That one was very wrong. I forget the name? Posited collective heavy electrons somehow? Anyway, even that theory had the nuclei emitting gamma rays, and tried to explain that most (not all!) were absorbed in the material.)
So when I say "it's really really firmly known that nuclear transitions emit hard radiation", I'm not saying that from a position of stick-in-the-mud ivory-tower dogma. I'm saying that because it's true, everyone inside the ivory tower knows it's true, and everyone
outside who bothers thinking about it also knows it's true.