I'm still waiting for a good, cannon poly relationship, but I'm not sure this is it.. Kaname I think is a lot more observant than the personality she displays, and I think she has an ulterior motive here. Whether it's because she knows how Nakatani feels and doesn't return those feelings, I'm not sure, but that's my theory so far.
Maybe she's playing match-maker for Piyo and Tsubaki, or maybe she wants Tsubaki for herself. Or maybe she's totally straight and just likes to help people make friends and just gets a whole bunch of amusement from teasing her friends. Like Piyo. Yeah, that's what I suspect; she's just a chaotic-good type person.