Its a stick they found in an area being actively examined, next to megafauna bones giving the age, that on inspection would have shown burn marks and probably not the megafauna lunch they thought it might be.

Birthday paradox? I guess it might originate from a similar but now extinct ritual, rather than the modern documented one. But given the near infinite number of potential rituals, it seems reasonable to suggest that because of the similarities it has been passed down over the 12,000 years. Even if the original ritual would be completely unrecognizable apart from the remaining similarities and performed by a different tribal group. Or maybe that is like claiming modern druidic rituals have been passed down for thousands of years.