I know it's a TV show and not a documentary, so artistic liberties are taken, but I imagine they want to be as faithful to history as possible, so is this true?
This recent thread featuring u/iphikrates may answer your question. Briefly, because the Trojan War and the description of it in the Iliad are entirely fictional to begin with, there's no particular standard of "historical accuracy" that makes any sense to apply to it.