My own take on this:
There is no such thing as an "average person." Averages are statistical abstracts. While the average peasant may have str 11, dex 10, con 11, int 10, wis 11, cha 10, the village supposedly inhabited by this "average" peasant may not have any individual peasant who fits that description. It probably has a peasant with Str 15, Dex 7, Con 11, Int 9, Wis 13, Cha 10, another with Str 13, Dex 11, Con 8, Int 13, Wis 7, Cha 15, and another with Str 9, Dex 11, Con 9, Int 17, Wis 12, Cha 8. Each of the peasants will have their own story and their own list of skills and feats that they've chosen in accordance with their interests, discipline, and desires.
(And despite the supposedly bell curved distribution, there will be very few peasants with less than an 8 con--most of them died in childhood accidents, plagues, or childbirth).
In this world, "adventurers" are not a separate race of people. They are those who by temperment, choice, or circumstance, took up the role of "adventurer." When the Shieldlands were overrun, most peasants fled, many were enslaved, and some were trapped behind enemy lines but not captured. That last group--those who chose to remain behind as resistance fighters, those who had no choice but to remain behind (because their escape route was cut off), and those who escaped slavery are the "adventurers." Some of them are stronger, faster, tougher, smarter, wiser, and more persuasive than the others. Others of them are none of the above but were just lucky enough to survive (the 14 dex rogue may dodge one blow in 20 that would have killed the 13 dex rogue, but there are probably 5 of those twenty blows that will kill either rogue and if the 14 dex rogue is unlucky enough to catch those rolls, it's the 13 dex rogue who'll survive). Still others are doomed (because of lack of skill, foresight, wisdom or luck) to be among the many victims of the occupation--their corpses displayed as warnings to others and their skulls paving the road to Dorrakka. (Some of these unfortunates will have died with the first arrow, others will have sold thier lives dearly but this group is all dead--both the high stat and the low stat ones).
So what does that mean for PCs? It means that the pool of "adventurers" is not that different from the pool of non-adventurers. Just as some peasants are strong, smart, and good looking and others are weak and unhealthy and are doomed to struggle their entire lives, some adventurers are tall have bulging muscles, cleft chins, wise minds, and gleaming white teeth, while others are weak and sickly and drag themselves along the bottom of the adventuring rung until fortune smiles on them (and they have the opportunity to loot the corpse of the white-toothed high-stat adventurer after the dire bear got him) or they become the NPC who dies in the opening scene so that the DM can show how evil the villain is. When I have the choice, the PCs are middle of the road adventurers. They're not the children of the gods or the scions of the master race but neither are they the whipping boys of fate. At 25-32 point buy, they'll show up their enemies through teamwork, skill, luck, and superior experience rather than because it's their birthrite. And some--perhaps many (especially at the level 5-8 breakpoint between low and mid level play)--will die in the process. Occasionally, they'll be shown up by "commoners" when they visit a town fair and assume that they're stronger or more skilled than anyone there (especially at low levels). But that's a part of the source literature too. (Robin Hood often found that others were his equal with the quarterstaff (from Little John, to Will Scarlet, Friar Tuck, and the Tinker) and Richard the Lion Hearted was slain by an anonymous French crossbowman).
In my view, point buy doesn't serve to set "adventurers" apart from "peasants." Instead, it serves to put all of the PCs at a more or less equal level in the adventuring community (so that party is playing the Hobbits in the Fellowship or Boromir, Legolas, Gimli, Aragorn, et al but nobody's stuck playing Pippin while everyone else gets to be cool) and (at 25-32 points) to place them firmly in the middle of the adventuring community so that some people will be more statistically endowed and others will be weaker.
