That is not an issue, because the tree will have been absorbing freshly made atmospheric carbon-14 until it died, at which point it starts to decay into carbon-12. So carbon-14 dating pinpoints the time of death, if you get the methodology right. We apparently now use accelerator mass spectrometers to just outright count all the atoms of c-14 and c-12. But in the 70s c-14 dating was notoriously tricky and full of pitfalls to with calibration and contamination and estimation, and it looks like we've only reduced the last of those possible sources of errors, the need for estimation, and the rest of it is still sketchy.