@Yunefia No, she was right. As they say, curiosity killed the cat. Yeoryeong was only asking because she was curious and they were involved in that stuff just now, but if they're not gonna be after them then it was correct for the MC to not let her hear it.
Be it Yeoryeong's kindness as a heroine or the way novels work, they're definitely gonna get involved somehow. If she truly cares about her friend she'll try to keep herself and Yeoryeong away from it. You can't just say the MC should let Yeoryeong do as she pleases and mind her own business...this'll both hurt Yeoryeong and she'll just be doing what she knows is right just to save herself but not her friend.
Plus, if Yeoryeong truly wants to know she can just refuse Dan-I. Dan-I just said they don't need to know, conveying that they should not involve themselves any further. One doesn't act like this out of selfishness, it's usually through love. She made the mature and hard decision here and decided for Yeoryeong's sake too cause she knows what's right and she worries. No matter how bad that might sound, mothers do it all the time for their children.