You miss my point. Aragorn doesn't cast spells, but he is definitively super-human. He lives for like 200 years and can heal people with a touch (at least, the "hands of a king" are ascribed particularly potent healing properties). Yet, none of these qualities are segregated out from the norm as "magical". They are just a natural part of the world he lives in. Likewise, he lives in a world where birds can talk, but this isn't considered weird or magical, only natural and normal.
The idea that "magic" is something that only comes from "spells" which are used by "spell-casters", while things that are not touched by this "magic" are "mundane" and thus bound by real-world physics, is a paradigm that is practically a complete invention by D&D. It isn't even totally true within D&D. D&D still presumes things such as giants and gryphons which are not possible within the framework of real-world physics, yet are still a natural part of the world.
Going into the topic of whether or not D&D heroes can be based on the likes of Hercules and other mythological demi-gods, it is worth pointing out that the monsters they fought (the Hydra, the Minotaur, Cerberus, the Chimera, etc.) were all demigods as well. And yet, all of these monsters are considered perfectly acceptable opponents for D&D heroes, if not downright plain or ordinary ones. Heck, Giants are based in part on the Giants and Titans of Greek and Norse myth, who were equals to the gods themselves, if not their direct relatives.
Given the opposition they go against, it is silly to say that a high-level D&D party are not themselves demigods, at least in terms of power.