It seems that this portion was published in the Watchtower in the year 1977 (as I have in the Spanish version):
The radiocarbon dating method has been widely accepted by many scientists as showing that humans lived back to at least 50,000 B.C.E. That conflicts with what the Bible says.
But physicist R. Brown of Andrews University claims that this radiocarbon dating method is highly inaccurate. After a ten-year study, he concludes that radioactive carbon atoms did not exist in the earth's atmosphere in significant amounts before 2000 B.C.E. and so cannot be used to date objects before then. Sometime around that date, he says, a major atmospheric change likely occurred, resulting in the buildup of radioactive carbon in the atmosphere.
One such vast change was the flood of Noah's day, which the Bible indicates to have taken place in 2370 B.C.E. That catastrophe without a doubt drastically altered atmospheric conditions.Gen. 7:11, 12
I don't know who is R. Brown, but I would like to find his "ten-year study". Do you know about an article comenting about it? As far as I know radiocarbon dating measurements have not reported such a drastically alteration of atmospheric conditions around 2000 BCE. The measurements does not report such a gap. So, we have two options, most scientists working in radiocarbon dating are liars and stupids, or this guy R. Brown was dead wrong.