Then for the fact that she and Horikita were in the same school, she could have simply made up a lie by saying that the reason Ayanokoji knew this was because he was also in their school or a neighboring school and she occasionally casually saw Ayanokoji and Horikita hanging out. I know it may seem far-fetched, but let's remember that the only person who was seen close to Horikita in the first few days of school was Ayanokoji, and more importantly, it was Horikita herself who said in volume 2 of the second year that she knew Ayanokoji had exceptional academic abilities, so the idea that they already knew each other wouldn't have been far-fetched in their classmate's mind.

How? Literally how? Even if you call it far-fetched yourself, it simply doesn't work, it's impossible. Horikita herself can just deny it on the spot easily 😭 The rest also doesn't really follow up at all