I mentioned it because as far as I saw they did not specify what coin they used.
You haven’t actually read the article, have you?
(…) the authors of the new paper conducted 350,757 flips, using different coins from 46 global currencies to eliminate a heads-tail bias between coin designs. (They also used a variety of people to rule out individuals with biased flipping techniques corrupting the results.) Regardless of the coin type, the same-side outcome could be predicted at 0.508, which rounds up perfectly to Diaconis’ “about 51 percent” prediction from 16 years ago.