Well, let's not put it past Ocean. As much as we talk about things being plausible, he will stretch what is probable to fit his agenda. We already know the cabin is located too far to drive to for a day trip, but close enough to walk to. Compared to that, rumours will be Ocean's 'get out of jail free' card. "How did they knoy THAT? ...oh right that person in the background ...rumours." It's quite a clever mechanism. Any important event, we'll have to think, what it professor plub or colonel mustard?
As far as Nika's reputation, there are parallel lines in the game concerning that. One is Nika is going to be a rising star of the team, so he'll be exposed to public scrutiny, triggering panic attacks etc. What better way to expose him to panic attacks than rumours he has no control over? He suffers one in the middle of an important game maybe? Then there is is record, he's been charged, even if the charges were dropped. Ceril has it out for Bella, rumours (such as assault or theft) will give her excuses to investigate Nika. Reputation will confirm her suspicions to start tracking him.
And don't forget Emilio deals in rumours. He sends Desiree out to dig up dirt, she's there behind the reporter.
Looking at each independently is wise, I don't think there's a specific orchestrator of a smear campaign (although Sasha's 'maybe he did deserve it' comment about Nika getting locked up suggests some people have axes to grind.
First instance - there can always be someone else listening in. It'd just be poor form. Nora is likely to start rumours just by speaking anyway, even if Miriam tells her off. Nora probably wouldn't consider it gossip, because she's telling the facts ...she's intentionally designed as a character to be flighty, ditzy and loose lipped. But we know Robin mentioned it herself to people at the bookclub, so there's the chance that the rumours have multiple sources.
Second instance, yeah, can't imagine any of them signed non disclosure agreements. JUst a guy being locked in the locker rooms would be enough to joke about and be in their social media feeds. Surprised there's no post on aurora of Nika in handcuffs yet.
Last, consider that Bella's absence is noted by the girls, and that's a pretty minor thing, but her going out with Nika is an established fact without NIka, Nami or Bella having said anything publicly - except for Nika at the bar, talking with Ayua, Trey, Jeff, Damian - oh and Robin's there. So imagine Sai turns up with a face looking like a split tomato, and Nika's got a split lip. Even NOra will put two and two together. Even if no one has seen it other than those, everyone would be asking Sai what happened, just like they asked Nika. And Jeff knows about it from the hallway moment and the bar talk. So there's no NDA's here either, and people don't need to see the event to start a rumour.
Nadia also owes a favour depending on your choices (ie not on Bella's path):
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Well, with what Bella writes on Mario's car, the whole basic plot to get Stefan cucking Mario, it's already decided that Nika and Bella are trying to do that in some form.
Further on that, from WiaB we know the Holgerson's had a 'paper' business, and the parents were resisting digitising it. I suspect paper means newspaper, not a paper mill. That might mean the reporter is Stefan's employee.
Halfway through this reply, I realised I should mention there are more rumours. Kate already calls Bella Nika's girlfriend the night after they go to the diner (if you get that locker room scene because you didn't kiss Bella). Vanessa also knows things. And not all rumours will be based on Nika.
We also assume Emilio is on our side, but we don't know anything about Emilio other than he's for hire these days, which presumably means he's had a falling out with the Zanes.
And for all we know, her character exists only to gossip with her smirks. But if this is the grey dyed version of the brunette we saw earlier with Sasha, she talks with Coates in the mensa. So she might actually have a serious plot.
Oh and I missed this one:
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So we don't know which rumour, but given Robin's embarrassment, it's probably the one about her, so yes, she did dpill the beans.