I've shot and killed black bears with a slug gun. Hunting not self defense. I did take a rather large male black bear at a quartering shot thro the shoulder and it raked thro him lodging against the back thigh bone. I use brenneke gold 3" mag slugs they're 600 grains. No bear alive can take one in the chest thro the vitals and live. Bears are not bullet proof. Many grizzlys have been takin by rimfire. Many inuit use 22mag for polar bear. Not my choice but it has been done. The bears I've shot have all dropped on the spot. The large male I spoke of did get up and take off. Again shot anchored him he was about 90yards when first hit. Buy a premium slug and shoot for the head spine or shoulders and start the fire bear huntin aint catch n release
Your observation as to where to shoot is bang on. What one shoots with is a secondary consideration to where to put it. If shooting for your life, refrain from using the chest shot. Sure, it'll kill the bear . . . eventually, but that is small comfort if you die. Nobody wants second place in a dangerous bear encounter. In a defensive shooting scenario, your goal is to stop the bear's forward progression which prevents him from touching you.
"If he can't touch you, he can't hurt you!"
That is the simple premise behind bear defense, but what is simple in theory can be complicated in practice. Thus we pre-program ourselves to a certain course of action, which will save critical time when we have to react. Defensive shooting suggests reactive rather than proactive shooting. If you are proactive, you are hunting; seeking out the action that you know will come. By definition, bear defense suggests unexpected, sudden action at very close range. The bear may appear suddenly without warning of his presence, and if he is close enough to be a threat the range is short. The shorter the range the faster things unwind, and the more difficult it is to make a precise shot on a moving target. If you need to have a discussion with yourself as to how you should respond, you're out of time and you won't prevail.
Another problem common to the majority of North American hunters is that they are pre-programed to make lung shots. The lung shot provides a target that is large, the shot is nearly always fatal, and the animal dies quickly, though seldom instantly, in a relatively humane fashion. The hunter who finds himself in a dangerous bear situation may hesitate to choose a shot that he knows will inflict pain rather than having a reasonable expectation of killing cleanly, despite the fact that breaking a supporting bone gives him the time needed to make a kill shot. Thus if you anticipate using a firearm as a defensive weapon, you need to train your mind to the reality of the problem as well as sharpening your prowess with the tool, be it a shotgun, rifle, or handgun.