Well, I'd say all the engine-out training I received as a student naval aviator, and the many hours and hours of emergency drills and simulators in the Navy and in commercial flight training came in very handy in those situations where I've encountered systems failures or indications of a fire in flight.
Jimmy Buffett was invited to fly with the Blue Angels, back in the 90s. As part of that invitation, he had to go to DWEST, and get trained up on ejection systems and emergency egress drills, helicopter dunker, etc.
Not too long afterward, he had a bad water landing in his grumman seaplane, as (IIRC) one of the small wing outriggers caught a wave, and the touchdown ended up with sort of a cartwheel. He was able to get out of the sinking, inverted aircraft, and he attributed his survival entirely to the training the Navy had given him. He said he'd probably have panicked and not had any idea what to do, if not for the dunker training.
I know that being forced to swim a mile in a flight suit, and tread water/drownproof in inert kit taught me that I could stay afloat for quite some time, as long as I did not panic. This came in handy once, when I had to go into a lake after a woman who was in distress a couple hundred yards out, and again when I got ejected from a duckie kayak while on some whitewater.
So, it seems to me that training has definitely mattered in some high-risk scenarios; it also seems to me that it is considerably more practical to get training, than to get experience, when it comes to some things.