Kuhn ran cross-country the past two years, so he had a foundation. He ran 5,000 meters in 16:33 in finishing fifth at the Greensburg Regional, although he was only 99th at semistate.
Given this I'd say two possibilities:
1) He's done some pretty solid cross country training
2) He is just a general monster than can run 16:3x as a speed guy off limited training
Forget the baseball, it might have done a little for keeping him in touch with speed and working on it, but some sprint work is not that specific for 800. I'd imagine basketball or soccer is better 800 training than some baseball sprinting.
It's pretty likely that the cross country training has done something for him however, and definitely pops the no training idea.
It's correct perhaps to say he had no formal 800 training, but prior to running these 800 times he was already reasonably legit as a runner from his XC. Take a fast kid with some aerobic base, and add a few 800m races + some 800 track training and I can see a really talented guy running 1:50.
Bottom line: If it was just baseball, I'd be fairly comfortable saying no real training. Given the fact he ran XC for several seasons and is a 16:33 5k guy...it can't be called no training. Regardless though the time is very impressive, especially given his limited track background.