Interesting topic. I have not had any formal training. I was in the military, and even spent some time in Iraq. I wasn't anything special, so received no special training. Lately, however, I have been doing the same thing I do here, but on the topic of survival and bushcraft, basically that means I belong to a few forums under those topics and participate in them about what I participate here. You can learn a lot from the internet. I also go and practice skills to hopefully become more proficient. Bushcraft and Backpacking seem to be two different topics, although there are a lot of bushcrafters who backpack. I believe that you can take the good of each and make something better.
In August, I took my boy scouts on a wilderness survival campout where they built their own shelters. Last month, we practiced making fire without matches.
Survival is something that both have in common, although they talk about it differently, and sometimes have different approaches. There are a few skills I think every backpacker should have, regardless if they actually ever need to use it. Here is my list of skills:
First aid
fire starting
shelter making
land navigation
signalling