As an ex-RN, and past Mum of troubled teens, you have done nothing wrong.

If anything, you should be proud of yourself for teaching skills that lead to resilience and survival.

If you had not given this teen the confidence to survive in the wild, they may have ended up on the streets, which has a much higher chance of an unhappy ending.
You should be giving yourself a pat on the back, not castigating yourself. You are doing a good thing, continue to do it. You are giving these kids a valuable skillset, and building their self-confidence.

The mother is panicking and looking for a scapegoat, because it can't possibly be her parenting that is to blame here. The fact that her daughter ran away instead of talking to her speaks volumes. You are part of the solution, not the problem.