Shitty job at localizing/translating then since he's always going on about curses and being cursed in his own game. It seemed an intentional word choice for people familiar with the NG series.
I was wondering if it was a slip like the God of War Poseidon thing that ended up being the last PSP game.
I don't think Ayane is Mugen Tenshin. She was raised in the Hajin Mon clan by Genra. She might be now, but she's always been an outcast because of how she was conceived and who her father was.
Ayane works with Hayate because, and this is just my take, she is envious of her half brother. Ayane was the product of rape and is jealous of Hayate and Kasumi for different reasons.
Edit: Just read up. Hajin Mon was a sect within Mugen Tenshin, just like Anbu is within Naruto's world. So yeah, she is Mugen Tenshin!