The thought has never crossed my mind, and it would have never crossed the minds of anyone I know. I have no urge to cheat and neither does my partner. I have generally thought that it’s a very unusual and uncommon phenomenon for someone to cheat, and I find it surprising how many people here think otherwise
First, make sure you’re never alone with her. It’s important to have someone be able to vouch for you that nothing bad happened. Even if it’s not her intention, rumors spread and mutate in the most unexpected ways, and you’ll want to make sure you’re in the clear if it ever comes to pass that people start to suspect that you are having a relationship with her.
Second, you’ll want to speak with her. Make it clear that you are serious and that this is a serious talk. Whenever you see her next, just say something like “we need to have a talk.” Might be cliche, but the cliche aspect of it reinforces the serious nature of it IMO, since most people already associate that phrase with something serious.
You don’t need to be rude, but you need to be very clear where you stand on the matter. Make it clear that 1) you are not in a relationship with her, 2) you do not wish to be in a relationship with her, 3) you don’t appreciate her saying that you’re in a relationship with her. With talks of this nature, there’s no point beating around the bush. She may be temporarily hurt, but there is a difference between being hurt due to rejection and hurt due to injustice. She will come to appreciate the honesty in time.