The character may lack the concept of level, but that's also not axiomatic.In no way does that tell you his level. It tells you his fighting capability. Level does not exist in the game world.
See, the combat capabilities are linked directly to level.
In some games, most notably AD&D 1E, but it's not alone, until one has both the experience and the training, one does not level up. Given that the training cannot be taken until one is in the level prior to the one trained for, clearly level is accessible in game world to some degree... "I feel it is time I learn the Fourth Secret of the School of Defense" is equivalent to "I need to learn to be a 4th level fighter." "What belt have you earned?" is a modern real world equivalent.
As is "What Rating do you hold" in the US Navy... and isn't actually tied directly to rank. I know that if I see a guy with a wrench and propeller and a single chevron, he's passed the standards to establish that he can do a certain range of aviation frame and skin repairs, and system installs/uninstalls/swaps. He may hold a higher rating than his insignia correspond do - asking him his rating will reveal that. (A buddy of mine was rated as a AKC, but only held the rank of PO2, so his worn badge was AK2. Yes, I've seen his DD214 and seen the AKC rating. My Grandfather was rated an SN1 during WW2, but didn't have the time nor boards to be promoted to PO1, so he wore SN2 until he outprocessed.
The concept of levels isn't something that exists only as a metagame; it exists in many administrative systems.
For yet another, more concrete, example. An apprentice electrician is a fetch and tote, and follow directions as given. A journeyman is able to work with indirect supervision. A master electrician is capable of unsupervised work, and of supervising apprentices. In those unions that still have them, a grand master electrician is one who scrutinizes the journeymen for admission to the ranks of master electricians.