I guess we won't know if that's what was used (and maybe even provided as part of the prompt given that both Alpöge and Mathew are mathematicians) since they decided against sharing their Fable conversation and instead opted for a memey tweet as their avenue of publication. We really ought to normalize full transparency in how results come about.
Anyway, if I read Tao's post and comment correctly, there's still a gap from the Vitushkin construction to a counterexample, but chances are that was in the training data. In general, it is just a serious problem for their practical applicability that the models are outputting proofs with absolutely terribly reference hygiene.