radiation - Nuclear decay rate affected by sun and quantum randomness

If nuclear decay rate were affected by sun, then emission probabilities would be subject to sun state and its influence, so quantum randomness would depend on it, Would it still be truly random?

One could argue that randomness would keep intact when consider the whole system..

But what about a non-isolable effect? what if there is no way to "define a system" without a sun/star influence?

If a variation source were found (for example neutrino emission) then perhaps it could be generated intentionally to control decay rates. Could we be sure that emission probabilities would never could be controled to reach 0 or 1?

Thanks for reading