I am extremely dubious regarding the claim that it has been absolutely dated to the 16th century BC. Two reasons. First reason is that in order to be absolutely dated one must date the wood by cross dating with an extant tree ring chronology. I do not think that such a tree ring chronology exists for olive trees. The second point is that if it was absolutely dated then we should know the date of its last growth ring which suspiciously has not been reported.
It looks to me as if this is an article of confused publicity. They have found a new olive sample and recently researchers such as Pearson et al have shown that Thera was in the 16th century. And so the article has conflated the two points. Now it may indeed be that the wood has been radiocarbon dated by Tuscon in which case it would return a radiocarbon age which could be calibrated to either the 17th or 16th century BC depending upon whether one uses the IntCal 13 or the suggested new calibration curve of Pearson et al.
I have done a quick search for a paper on this news article and cannot as yet find one which makes me also suspicious of the claim.
Jonny
The path to good scholarship is paved with imagined patterns. - David M Raup