There's also a reason why Mina literally propose a throuple to Hana after the party in the update before the last one. As for the birthday party, I keep repeating the same argument but let's write it again: characters and circumstances evolve. Just because Hana said she prefers exclusive long-term relationships doesn't mean she'd totally exclude a throuple with Mina and Edwin as a (oh wait) long-term relationship, exclusive to two people she is attracted to and like.
The reason why the game counts if Edwin cheats on girlfriend Hana might just be because it's too early in the story, and she doesn't even know about Mina and Edwin when the choice to be her boyfriend comes up. With the 3 million branching paths there is in this game, it's fair to assume that, while cheating on girlfriend Hana might lock up a possible throuple with Mina, keeping her as a fuckbuddy doesn't lock up that possibility, because their relationship is still sort of open to changes.
And no, the general situation points towards lasting throuples on choices related to Mina and Ewin's relationship, Hana and Edwin's relationship, Hana and Mina relationship, and Mina bi-curiosity points (maybe also Hana anger points). I don't know where you got this "throuple only on corrupted path" idea from. I literally don't understand where it's coming from.
Yup, this is why I rarely write in here. You guys are hopeless.
I'm done.
Not even going to search for a fun image to represent how done I am.