Pooh,
A stingray barb can be a few inches long. It's unlikely that anything but an extremely unlucky jab would puncture anything bad enough for the wound itself to kill an adult human, but a chest or head puncture plus the venom/poison could easily kill someone. Stingrays don't have a rep as man-killers because people usually just step on one and get nailed in the foot or lower leg, and that is extremely painful but won't usually kill. Even a small child will usually live from a stingray jab in the foot or leg. But in the chest... That would be bad.
He was probably chasing one down or trying to handle one and it got pissed and whipped the barb into his chest. They are almost never aggressive with the barb unless you step on one or it feels very threatened or trapped. I've seen videos divers attacked by stingrays, but in those cases the stingrays never even used their barbs. They just did the whole smother and try to suck your arm or face thing which is essentially harmless unless you overreact and provoke it into stinging you.
At sea world, they used to surgically remove the barbs from stingrays that their divers would handle during shows. I don't think there is any safe way to handle a stingray that still has it's barb because if you're touching it anywhere (except firmly holding onto the tip of it's tail) it can stick you.
I swam around stingrays on numerous occasions while growing up, and I never dared swim closer than about 6 ft. I'd mess with the little sand sharks but pretty much left the stingrays alone.
Some divemasters and dive tour guides will do a feed-the-stingrays bit but those rays have usually been conditioned by repeated exposure to divers, so they're a lot more tolerant to being touched and fed. I wonder if that's what was going on here.
As a diver I admit to being curious about the details and I'd like to see the video from an educational perspective, but I doubt it'll ever be shown in it's entirety.