There's nothing wrong with radiocarbon dating per se, and not even with dendrochronology per se -- it has to do with the screwed up pseudochronology of the eastern Med.
The problem with the UluBurun wreck was, they couldn't get a wiggle match that didn't prove that the ship wasn't built for centuries after it supposedly sank. At first the results looked great, then the full import of the dates involved "sank in" and the dating was rejected by most. The reaction was not unlike what Zahi "Zowie" Hawass said recently.
sidebar:
I never pass up Greek/Roman stuff — I love it — but well it’s been a long day & I was being flippant — you know the blogall warming stuff & all that.
Thanks for info though. I just remember that I thought Troy was around 1200 and really was not aware of the intense debate.