Carbon dating is accurate
I agree radon could influence the Carbon 14 in the organism, because radon is quite radioactive, but luckily there's way more carbon 14 transfer than radon transfer in a given environment thanks to the carbon-nitrogen-oxygen cycle.
An organism's exposure to radon is a possibility; an organism's exposure to carbon 14 is a necessity.
Carbon 14 is unstable and therefore its age is measurable.
The resolution of this debate is whether or not Carbon 14 dating is accurate.
Because we have already demonstrated radiometric dating, we can take something that is of known age, like a biological relic or some ancient item made of organic material like wood, and subject it to radiometric dating.
Another assumption is knowing the Carbon-14/Carbon-12 ratio in the atmosphere at the given time it died.
This changes as time goes on, and there is even abaration in our own atmosphere. With an unknown ratio, it is impossible to determine how much Carbon-14 has decayed.
If we have an item with unstable carbon, carbon 14, the atom does not have enough electrons, and given the unchanging rate of decay of carbon 14, we can tell by its instability how long it has been decaying from the parent isotope.
So a non-decayed atom's nucleus would be stable and would have all of its electrons.
Search for carbon dating is accurate:
To predict the age of a dead organism, you must first assume that it has been undisturbed for however many years you conclude it to be.