I'd have a conversation with her about this at a calm time, when you both aren't stressed about it. Explain to her that you do admire her independent spirit, and that you are also disappointed when she refuses your help but then chooses (and yes, use that word, *chooses*) to blame you for her mistake.
If it were me, I would ask her to let you help her at just the beginning, to ensure that she does understand all of the directions and at that point, she can show you a proposal of how she's going to organize her project/work times to get it done. Once you are both in agreement, she's welcome to proceed on her own.
If she refuses to agree to this going forward, make it clear that she is *never* to blame you for her mistakes if she refuses help. Ask her, point blank : "How would you feel if I was making cookies and following a recipe, and when you asked to help, I said no. And then, when I made a mistake, I yelled at you and blamed you for it? You would probably be angry and frustrated and hurt, and that is how I feel when you blame me for mistakes I had no idea about. That's not a reasonable thing to do-- to blame me for something you refused to let me help you with. You don't get to have it both ways."
And if it happens again, I'd just stop her. "Remember our conversation about this? You are welcome to go in your room and be angry with yourself, but you are not allowed to stay out here and be mad at me. I did not create your problem. " and either she goes to her room or you go do something else in a different area. Sometimes, removing yourself from a person who is being unreasonable makes a lot of sense and keeps one's sanity.
And if this is a problem, ask her to "Explain to me how it is that your result/failure/mistake is because of me, because I am confused." Be sure to correct her perceptions. "Oh, wait, you mean when I asked you if you wanted help and you said no?" or "Oh, wait, when I told you to do X and you ignored me?" Maybe this will help her see how she's making her mistakes.
I like Flaming Turnip's suggestion very, very much as well.