That is absolutely possible.
However, I do also try to consider that what she may (or may not) have done would be something in her past. I strongly believe in second chances, even for really egregious mistakes. But you don't get many additional chances if the mistakes are really huge.
Plus, let's be real: extremely often, when there's a rumor about someone — they're impotent, they're a slut, they have a disease, whatever — it's based on a misunderstanding / misinterpretation, a half-truth, or even another rumor. I think that's especially true in college (and pre-college school), where people interact with a lot of others all the time. Rumors tend to spread really fast in that type of environment, and rumors have a tendency to be like a game of telephone: each new retelling of the rumor gets a little change, and pretty soon the current rumor doesn't even remotely resemble the original one.
And before anyone cites the fact that Chloe moves decently quickly with the MC, in my mind it's very possible that she does this precisely because practically everyone sees her as a slut. I could see a possibility where no one really is ever willing to do more than try to get a quick score with her. Now you have the MC come along, someone who can be actually decent to her and treat her with respect and kindness. What's she supposed to think about that? It's possible she sees him as the only decent guy she's ever going to find, so she's really tempted to throw herself at him (despite the irony of doing so) to keep from losing him.
I've played both interactions with her. On a Chloe path, of course the MC believes her when she says it's not true, and he defends her at the dance. On a Nora path, though, the MC does the exact opposite. Since Nora says the MC shouldn't trust her, he doesn't. So I can see at least two sides to the story.