There a 4 hour video by Vertias that goes over it pretty extensively, but the TLDR answer is yes Billy cheated. If you don't wanna watch the whole thing then the first bit gives a good explanation on why MAME and arcade look different despite running the same code.
Billy submitted three scores for Donkey Kong that he purported to have all done on original hardware. The only evidence for these scores were VHS tapes submitted by Billy where they show obvious MAME signatures or eye witness testimony from people like Todd Rogers, another infamous cheat who had hundreds of literally impossible scores in the Twin Galaxies database.
After the MAME signatures were discovered, since originally when the scores were submitted no one really knew about that, Billy would spend years defending his scores as legit and oscillating between different defenses. Ranging from the tapes weren't actually his, arcade can look like MAME under the right circumstances, to the tapes were edited to look like MAME. All of that culminates in the Twin Galaxes lawsuit where Billy was sued for fraud for inflating the value of TG, that case was utlimately settled but did provide deposition footage of Billy state numerous provable lies about his scores as well.
