Guy's probably decided he's leery of getting into a relationship with a girl who's his half-sister as far as he knows, while the girl in question may have some strong suspicions that they're not actually related because their parents entered a marriage of convenience.
To be honest, if she really wants a relationship, she should help with the investigation first, which has a decent chance of proving they're not blood related. Girl may have more information she's hiding as well, similar to the fact that she forged that letter.