Carbon dating accurate range
Radiocarbon dates are certainly not precise to within a year or two, but they are generally precise to within a few hundred years or better.
The measurement, before calibration, came back with an error bar of /- about 60 radiocarbon years. It should be noted that these measurement uncertainties do not increase linearly as one goes back in time.
Thus it is possible in some instances for two samples from a few decades apart to have the same radiocarbon concentration today, and hence the same apparent radiocarbon age.
This happens whenever there is a wiggle in the curve at the time the samples died.
Modern radiocarbon dating uses tree-ring chronologies to produce the calibration curve.
Because the radiocarbon to stable carbon ratio in the atmosphere has fluctuated over time, there are "wiggles" in the calibration curve.