Paying her to be our day tutor also saves face and isn't so flimsy. Or, as Cannongerbil says, we could just stick to our altruistic guns. Your vote is a bit of an uncomfortable middle ground.
I'm not sure you fully understand what your vote is going to be taken as. If you asked me why someone is angry and I said "I'm not sure", your first thought would not be "oh, he must have a bunch of different theories and doesn't want to give one more weight than another", it would be "okay he doesn't know". That's a very bad impression to give here. Not "bad situation" bad, but "bad compared to lots of other options" bad. Making Kyoko's anger a mystery means she could be mad at anyone, and merely adding "but she isn't mad at you" means nothing when we've already claimed to not be sure and it reinforces the idea that Big Sis might be mad at Yuma. If we want her to believe us when we say Kyoko isn't mad at her we need to say something that indicates we have some sort of clue about what Kyoko's thinking. It being Kyoko's business does that, a specific but possibly wrong claim does that, vague prophecies of existential doom do that. Your vote does not.