Its perfectly accurate in terms of facts but where it runs awry is in the finer details of interpretation. What we consider homosexuality today isn't what homosexuality may have been 2000 years ago. Even today there are some (admittedly fringe) cultures where the act of oral sex between males is perfectly normal.

In crude terms just because you- Joe Ancient Athenian / Spartan- wanted to get your jimmies off with the guy you're around 24/7 because your wife is days away and otherwise there are no other accessible women, didn't necessarily mean you wanted to do nothing but get jimmies off with men. As it were, sex and orientation were two different animals. The primary difference was that where today we see two guys kissing and say unironically, "woah bro, that's pretty gay." 2000 years ago they'd have sex and still say, "Nope, not really gay. I got a wife and kids at home. Soz."

I'm hesitant to throw Christianity under the bus but I think that wider religious attitude wanted to lump sex, gender, sexuality, and who you want to jimmy into one amorphous blob where any one term is equal to any other.