Actually, that statement is pretty useless.
Radiocarbon variations over time are known because of tree ring studies, and studies of coral. The rate of variation is very small, but can make slightly older rings appear to be the same age as younger ones, because the C14 uptake was higher in the earlier years when the rings were grown. Samples from plants grown in soil higher in regular carbon (C12), such as volcanic ash, will appear to be older than they are, so samples of that kind are avoided.
Except at Thera, at Thera those results have been embraced in order to prop up the supereruption nonsense.
I had not heard of Thera before now, so I checked wikipedia, and it discusses pinpointing the date of the eruption using artifacts, and one single olive tree found under the ash. Nothing about a super eruption. What is the controversy?