I'm a foreman of a tree crew . One of my biggest on-the-job fears is that I'll be injured in a tree and have to be rescued by my men. Another is that one of them will be injured and I'll have to rescue them. It's difficult to do well and difficult to practice, and mistakes are costly.
I am willing to undergo the training you mentioned and my boss would probably pay for it (more info appreciated), but I think our whole crew is better informed than most in first aid, and some have rescue experience. Still, situtions like those described earlier are often volatile and demand clear thinking more than anything. I agree the primary thought should be DON'T RUSH.