A common misconception encountered in the discussion of C-14 dating is that, supposedly, C-14 can only last for 60,000 years, and after that, all of the C-14 in a sample simply "disappears". This is not the case. The carbon sample continues to undergo it's approximate 5700 year old halflife, growing smaller and smaller even after most of the readable carbon has been converted to nitrogen -14. It is true that after the 60,000 year mark, the sample is so small that it is no longer useful in radiocarbon dating or most methods of measurement, but that does not mean it has all decayed away into another isotope. It is still there, progressively shrinking. Astonishingly, the Old Carbon Project, funded by both the United States and Canada, sought to improve detection methods to allow discovery of the some of the oldest samples of natural radiocarbon conceivable in coal (180,000 years old!).
Thus the evidence seems to strongly suggest that the samples of coal used by the RATE Project were subjects of in-situ or in-lab contamination, and do not possess any levels of intrinsic radiocarbon that would suggest that the earth is only thousands of years old as opposed to billions, nor does their work in this area establish any viable doubts regarding the current methods of radiocarbon dating.