I'm the guy who wrote the blog post, and I want to offer some clarity. Usually when people say "Pythagorean" tuning they are talking about three-limit just intonation, not five-limit. In three-limit, the major third is indeed tuned to 81/64, which sounds pretty terrible. That might explain why medieval people thought thirds were a dissonant interval. Five-limit just intonation tunes major thirds to 5/4.