I guess i would have to say the correlation is only as good as your guess assuming the decay rate is a constant.
But somehow people will say " oh but it is constant"!
Well ... it is. This is one of the first things that was checked --- by the Curies, whom I presume you've heard of --- right back when radioactive isotopes were first discovered. They looked to see if the decay rate was affected by any environmental influences such as temperature or pressure. They drew a blank.
Throwing the sample into a nuclear reactor might skew your results, I guess ...
Besides which, we can check radiocarbon dating against dendrochronology and the formation of varves in proglacial lakes. In order for radiocarbon dating to be wrong, they'd have to be wrong too, which would mean that three totally unrelated processes would have had to go wrong in lock-step with one another.