W.P.
Dear M.:
If you think that 50-50 is a good idea, go for it. No comment here.
Yes, I have heard my share of 'it was your fault that...' from my son. Very similar cases. In your example, I would say 'No, I made you get your xyz, but I did not tell you how to do it and I did not ask you to hurt your abc.' Her reasoning is that without your 'order', she would have not been in that situation. That is actually pretty smart, because it is true. But you want to teach her responsibility for herself and for how she performs tasks. If you told her to cross the street, she would still have to make sure that no car is coming. That's the route I would go: Explain to her that she has a given objective, but her way of achieving it is largely up to her, and she needs to take responsibility for that.
If you want to be more explicit, tell her to stump her toe. She probably won't do it and look at you puzzled. Then tell her that if she won't even do it on purpose, how can it be your fault when she does it by accident?
Regards,
W.