It does apply, in some cases - it's actually a preference.
For small game such as rabbits a neat little shot to the head with a high powered air rifle will kill the rabbit and save you from having to get the shot out afterwards. This is also most likely with small game that it's going to be much harder to pick out heart or lungs to aim to, the head is a clearer shot.
For larger game there is the choice, deer, as in your example, stand high in the grass and it's much easier to pick out where the heart or lung shots would be.
The reason people often pick heart or lung shots, especially with deer, is that a single shot kill is much more humane, and responsible, than having to shoot twice. The pro to shooting for the brain is the death should be instantaneous, the con is the target size... if you miss you'll spook the deer and it'll flee.
The choice of shot will also depend on distance, bullet, your shooting ability, weather conditions...
As for humans, well, a good shot anywhere can cause us to bleed out and die. It's almost the same preference - a head or chest shot can kill a person, but you're more likely to survive the latter.
This article is quite interesting: outdoor life - where to shoot a deer for one shot kills