If you punch enough little holes in something living, it will die given enough time - time a victim may not have. What good is killing the animal if it kills you in the process, or you die before you get to medical treatment? In the referenced article, the couple was lucky that the bear didn't take the bite it was close enough to deliver. Had that happened, at least one of them would likely have died.
The idea of large-bore weapons is to punch one large, deep hole in a critical area. Additionally, while the shooter was able to get off seven shots into the bear without hitting his clients, the chances of him hitting his clients went up with each shot. And it's a good thing the bear wasn't coming from him - because he may only have got 1 or 2 shots off before the bear was on him. Then what?
The energy imparted by a single large-caliber bullet at high velocity will do a lot of damage. If the guide had been carrying a larger bore, such as a .454 or maybe a .44mag, the shot to the neck may have been the only one he would have had to take - maybe one more follow up to center of mass to hasten the process. A .454 Casull will deliver up to 2,000lb-ft of energy whereas even the BuffaloBore 9mm +P 147gr only maxes out at around 400lb-ft. A .44mag heavy BuffBore +P - if you can find a firearm that can safely handle the pressure - delivers about 1600lb-ft.
I'd much rather be prepared to make one good shot to a critical area - the face, behind the shoulder, base of neck, rear of skull - than have to rely on emptying my magazine, consistently maintaining a clear field of fire, and risk being low on ammo deep in the backcountry. Strength and accuracy can be remedied with exercise and practice - two things you should be doing anyway if a) you spend time in the backcountry and b) if you own and regularly carry a firearm. Know your firearm, and know yourself. If you're 110lbs soaking wet and have wee hands, a 10mm semi-auto double-stack G20 may be more gun to handle than a .44mag Vaquero.
Before the advent of the repeating rifle, hunters, explorers, and fur trappers went into the wilderness with .50cal+ musket ball or black powder rifle. And they "loaded for bear" when they were in bear territory - meaning extra powder for higher velocity. And they only had one shot to kill - follow-up shots were impossible with a single-shot muzzleloader.