So, a few things on this.
With the usual caveat that every table can run things as they want, I very much have to disagree with the last statement. AFAIK, while PCs are "exceptional individuals," this is represented in the game (and in all editions) by being ... well, exceptional. And you can't measure exceptional unless you have a baseline- in other words, what are the stats of other people/gods/heroes (early editions) or everything, including monsters (3e on). The game would cease to make any sense at all if the exact same numbers represented something completely different for PCs than they do for NPCs, as you can see if you think about in terms of anything else and rephrase it:
"Maybe we just overdramatize the impact of that 8 for hit points? I mean, PCs are usually exceptional individuals so maybe 8 hit points is actually average? Maybe 8 hit points represents something completely different?"
When PCs have a difference (for example, if you use death saves for PCs but not NPCs) it is spelled out mechanically. There is no mechanical difference in saves, etc. for NPCs and PCs for their abilities, so this isn't the case. The idea that PCs use the same scale, but should have better abilities, has been there since the beginning (see, generally, Gygax's comments about alternate methods of rolling PCs in the DMG and later in UA).
To sum up: no, PCs don't use a different scale. If there is a difference, it is that PCs have more "points" in the point buy.
In addition, the default array for a standard commoner (non-special PC) is 10, 10, 10, 10, 10, 10. However, using point buy (which provides abilities that are, on average, slightly worse than 4d6k1, but without risk), you can generate, inter alia:
14, 14, 14, 10, 10, 10 OR
14, 12, 12, 12, 12, 12 OR
13, 13 , 13, 13, 13, 10
Now, since you're a special PC, even if you're just a regular ol' human, you can start with, inter alia:
14, 14, 14, 14, 14, 11 (or something else)
Which means that a regular ol' human PC can easily start with one ability above average, and the other 5 abilities WELL ABOVE AVERAGE than the standard commoner.
Whew. All of that means that for a PC to take an 8 (always to get an advantage in something else) is to go below the average for a commoner. To not just be not-special, but, um, well below not-special.
So in a way, this is the bane of both Roleplaying and, um, just playing. Because it's a common feature/drawback of many games. People want to take advantage of a system that allows you to trade having a drawback in exchange for additional benefits, but don't actually want to suffer the drawback.
If you don't want to have an 8 intelligence (say), then don't take an 8 intelligence.