His believe is that no one conceptualizes it as levels.
Indeed. They are not aware of levels. But they can be aware of power and experience, and difference in power and experience.
No matter how many rules there are that allow player(s) to narrow it down and find out the exact level and abilities of others, it is my belief, that this information is reserved for player(s) only (for mechanical reasons).
The PCs should understand things just as we understand power, and experience in real life. This means that things should not be as clear-cut for them.
For a 10th level PC, a 12th level NPC, is not a "character with two more levels than him". He is a character, perhaps more powerful, perhaps more experienced, more traveled, more recognized etc. At the same time, the PC might decipher that their difference in status is not one that puts the two of them miles apart in terms of power. If this 12th level NPC is an adversary, the PC might as well be aware that with some luck, or/and help, or/and clear thinking from his part, he could eventually win the competition/battle between them.
Now, if this NPC is a 16th level NPC, the PC's perspectives change. Now their difference (in whatever it is), is far more apparent, and the PC should somehow be aware that a confrontation with the powerful NPC should not be taken as lightly.
Moreover, despite what some spells and abilities might provide, I believe that the DM should not give the information in levels, abilities or anything number/rules specific, but he should provide the information as mentioned above, when possible.
I understand how this sounds weird. And a reasonable question would be:
"Why act like you don't really know, when the game's rules provides you with the exact numbers?"
Well... as mentioned above, if the DM wants to (for immersion purposes of course) he can give players the same real-life, vague and subjective information known to the PCs.
If not, it is up to the game group to decide collectively, whether they are willing to keep out their meta-game thinking and always react according to what their PCs perceive, by simulating real-life perception.
Of course, this is no RAW... far from it. It is just how I like my games
As for those who believe that there are levels in real life, they should keep in mind that, in real life, status is very VERY subjective.
In the game, a level is a level, no matter what one things of things, the numbers talk.
In real life, "levels" are questionable. Elections are won, championships are won, wars are won, PHDs are taken, careers are built, scientific accomplishments are claimed... but the apparent truth is questioned by many.
Steroids, injustice, diplomacy, fixed matches, stolen ideas, back stabs, propaganda, money, corporate benefits, lies... are some of the things that can uplift men to godlike statures... while these men don't really have the "level" they are supposed to have.
Even when foul play is not the case, people tend to have different opinions on people, and one that is an "aclaimend-something" for some, is nothing but a jerk for others.
NOT always... but it happens all the time...