Before her H-scene she herself confirms the rumors, that is correct, then an extra layer of proof is added when you see her exit a hotel with a client a little while later. But the conversation that Kaizen was talking about was a conversation between MC, Ayase, Yuka, and Chika in a restaurant, NOT the one between Chika and the MC in the MC's apartment.
This is where the "Not sure if I'm misremembering or not" part of my comment comes in as I haven't replayed that specific conversation (the restaurant one), but I believe that in the restaurant conversation she simply mentions that there are rumors going around school about her. Kaizen, was acting as if at that point in time, those rumors were 100% proven true simply because Chika mentioned them. She basically said something like "people are saying I have sex for money" and Kaizen took that as her pretty much saying "I DO have sex for money. It's 100% confirmed true." Kaizen was then using that as evidence that Chika's "prostitution" was already mentioned when at that specific point it was nothing more than a rumor.
My comment was pointing out how those "rumors" don't exist BEFORE that conversation in the restaurant, when Chika brings them to your attention. NOBODY mentions them UNTIL THAT POINT. Which is one of the reasons why the players are upset as it feels like it comes out of literally nowhere with absolutely zero buildup. When they get to the restaurant and Chika mentions the rumors, the average player (me included) is most likely thinking something along the lines of "Oh, they're just rumors, surely the story will involve us proving that they're false." Only to be severely disappointed when the story then proceeds to double down on the rumors by instantly confirming them to be true a short while later.
Also it's important to note that KS says the quotes around "prostitute" matter, so I don't know what the hell that means.