I've read some of those studies - as I understand it, they are not substituting for any significant portion of the feed (less than 1%), but rather are making the feed itself more digestible/absorbable, just as fermenting feed makes certain B vitamins more bioavailable. Ash used to be incorporated into corn for us humans to make it more bioavailable, too.
They also contain some trace minerals (and concentrated quantities of whatever heavy metals the previously green growing thing absorbed over its lifespan). Finally, there's a bit of the charcoal neutralizes all poisons snake oil - which oversells its utility more than a lot, though there is a tiny bit of truth. Many things not yet absorbed into the body will bind to the surface of charcoal and eventually pass out of the body in the feces - but what has already been absorbed will not be improved by charcoal, activated or otherwise. Its not good for strong acids, strong bases, and an actual list of what will and won't bind it is poorly known - even such common chemicals as alcohol are claimed to be bound by charcoal on some sites, while others claim it ineffective.
Vinegar's benefit is primarily to adjust pH. (Acetic Acid). If your tap water is already acidic, no need. Do a cabbage test.
You may also be thinking of biochar, which is almost, but not quite, the same thing.
My opinion? Makes for a neat youtube video, but its closer to magic than science, and not worth the effort at the scale of the typical backyard flock holder.
