Well, possessiveness is the one that won, so... about that. Though that is, of course, rather different from yandere, as it is only one of the elements that makes up
that psycho pie.
The question you should be asking yourself, though, is how much of that thought was
her. And you can go wild with it, because that question will only ever be answered from Hibiki's highly unreliable perspective.
To use this as a digression point on something I rambled at
@Flibspeak a few days ago about (albeit less coherently):
Hibiki is a
person. She is not simply an icon of her ideals and simple exaggerations of her main character traits. She is brave, and wants to help others, and impulsive, and likable. She has a tendency to act before she thinks, overdo things, and lie to the people she loves when she's hurting. She's dependent on others, more than is probably healthy, for her own self-esteem and for her general happiness. She's generally not very capable of denying her own feelings, whether or not that would be better for her (though she is capable of
hiding them).
But most relevantly, she's afraid of death, she's afraid of failing, and she's afraid of losing the people close to her. Those are
less important than other things most of the time, and those aren't things she'd like to admit to herself, but that doesn't mean they're not there. She gets angry. She is entirely capable of hate (you've actually already seen it in this quest), though in general she would feel absolutely terrible at herself for it. She's tried to straight up kill a dude before (don't expect me to believe that Ver would have survived a punch it took both Kirika and Shirabe to block). She is a very good person, but interesting character writing lies in flaws as much as strengths, and I'm certainly going to be using the former.