Bounded accuracy is a major feature of the new system. It promises that bonuses to rolls won't grow too much throughout a character's career. And indeed, a first-level fighter would have an apex skill of about +5 (Strength +3, proficiency +2), whereas a twentieth-level fighter would have the same skill at at most +11 (Strength +5, proficiency +6). Supposedly, such bounded accuracy allows characters to meaningfully interact with the same threats for most of their career, if they so choose. (Further reading.)
This wasn't always the case. In 3e, everything was modeled by the rules, and a level 20 character meeting a level 1 character would not require any change to the way either are represented by the system. Such interaction was unlikely to be meaningful mechanically, as level 20 characters would outclass level 1 characters thoroughly. Thus, level 20 characters in 3e were both in mechanics and flavor significantly more powerful in every respect.
In 4e, only the immediate vicinity of PCs was ever modeled, and there was no such thing as "level 1" people near them by the time they'd hit level 30. If they were to be modeled at all, "low-level" creatures would be represented as minions of higher level (For more on this particular reasoning see this blog post, though it's not that important to the question at hand). There were no conclusions of relative power level to be drawn from the mechanics, even though the numbers kept on growing, but flavor of becoming demi-gods at high levels preserved.
In 5e, it appears that the approach has moved back to modeling the whole world, as the implementation of flat math indicates. But what about the flavor? Is the world's greatest athlete at +11 really only capable of winning about 3/4ths of the time against a village strongman at +5? If that is not the case or the intention, how is this apparent disconnect reconciled? Is comparing them in such a way actually valid?
If it is, indeed, the intent of the system (please provide some quotes if possible) that even at high levels PCs do not straddle like colossi over mere mortals, it is a serious departure from the past two editions I'm familiar with. As a qualitative change, it would impact the way I treat high-level characters and the role they play in the world, much more so than different class features or spellcasting methods of a new edition.
Does the bounded accuracy approach mean that max-level characters are no longer demigods compared to starting characters in everything other than killing?