Imagine she was in a situation where she needed to get away and didn't have these skills, what would happen then?

She'd either 1) Not be able to run away, and be trapped in a situation that feels unliveable to her (HUGE risk for suicidal action there. or maybe she was in physical danger and would actually be harmed if she stayed?), or 2) Run away in the middle of winter without any survival skills at all.

And yes you showed her how to treat injuries. That is one of the biggest harm-reduction techniques taught to people who self-harm. That makes her safer.

Imagine how unhappy this poor girl must have been to be self-harming regularly and then leaving her home with no good place to go. If you gave her happiness and made her safer (which you did), then you did a good thing.