While it's not exactly the same question, I've covered a similar Egyptian drilling technique in this thread. There are several resources there that show successful modern recreations of drilling tech and images from dynastic Egypt showing them using that technology. It does also address claims from Petrie.

I'll add that the way in which this video portrays archaeologists dismissal of Petrie's claims (i.e. he's old and therefore wrong) is a typical way for pop science and pseudoscience authors to deflect criticism. Public audiences don't (and/or can't) evaluate social science claims based on accuracy; as I've touched on here, they judge them by their utility in a cosmological framework- "Does this make sense?" Because archaeologists operate with inductive logic, we revise our ideas with new evidence. This means that old ideas that "made sense" with the evidence available at the time might be discarded. If you only ever read the information from high school textbooks, you might never see that new data, and it will feel unjust or dogmatic to do away with the old ideas.