PCs and important NPCs have plot armor. And consequences are that plot armor.
When a PC chooses to take a consequence instead of being taken out, what narratively happens is the assurance that the attack, instead of having a random result that might include death (a well-aimed bullet can go through 4 stress boxes for example), will have the specific result of a nonlethal consequence.
Exactly like Fate Points, consequences represent the amount of narrative power the character has; they are forcing a random chance that might have resulted in death into a narratively interesting outcome. PCs are heroes and, beyond having a higher level of skill and power than common men, heroes also are tied to the plot and protected from the Law of Averages because we simply do not want them to be average; they are heroes. Hence their not being killed and taking consequences instead.
It is not that consequences would reflect something impossible; people have survived from bullets, explosions, grenades, plane crashes and other horrible dangers due to sheer dumb luck. Those results are unlikely - but possible. Consequences are one of the three measures of luck the hores have whith which to influence and direct that outcome.
