accidentally twisted truth-will reference bust me?

So, i had an interview recently with a place i would love to work, and most of the interview went great. we got along great, i am qualified for the position, and interested in their work. the only thing is, they asked me a question about how i deal with challenges, and my mind completely went blank. i dont know why, because i actually am good at dealing with this stuff and have had multiple good examples of me dealing with challenges! So i recounted something that happened this summer, but made it sound like I took initiative in remedying it when this wasn’t really the case (honestly it didn’t get remedied super well at all, just something we dealt with through the entire position). I didnt even realize that i had told them something a little twisted until after the interview ended! i seriously didn’t mean to do this, i think it was a combination of nerves, wanting to say the right thing, and a bad recounting/recall of an event. On top of this, it was something that happened at my past job, and my supervisor is one of my references

My question is; how likely is the recruiter to contact my references and follow up on this story? I still work with my old supervisor and would hate for her to have to get a confusing question about something that happened a different way than I said. I am also worried that would hurt my rep with her, and i really don’t want that to happen. Would it be better for me to just say i’m no longer interested in the position to remedy this issue altogether and guarantee the recruiter wouldn’t ask about it?

I literally cannot believe I did this. I’ve never even SLIGHTLY lied in an interview before and i have no idea why i did it now. It really sucks because it’s a job that i’d love!