3e, 4e, and 5e define Psionic as "magic".
5e Psionics officially casts "innate" "spells".
Even AD&D Psionic is defacto magic, and refer to various "spells".
The 4e Martial power source is explicitly "magic". The 5e Martial is defacto magic. 3e Fighter does impossible things − defacto magic.
"Spells" in quotes right? Not spells, but yes WotC made Psionic magic.
1E no. "they enable characters so endowed to perform in ways which
resemble magical abilities." from PHB. Resemble.
2E no. Complete Psionic Handbook
"Many people assume that psionics is just another type of magic. The AD&DR game already has two
types of magic-one wielded by wizards and the other by clerics. So it is not unreasonable to ask, "Does
the game need a third type of magic?" The answer is no, the game probably does not need a third kind of
magic.
But the question is misinformed because psionics is not magic. Magic is the ability to shape,
control, harness, and utilize natural forces that infuse the game world and surround the characters. It is
based on the principle that, through the use of words, gestures, and catalyzing materials of unique power,
these external energies can be controlled. The key element of that statement is external energy. Magical
effects are produced externally by manipulating outside forces. The power does not come from inside the
wizard or priest but from somewhere else.
Psionics is the complete opposite of this."
Your statement is incorrect, on all accounts.
No. Your statement is incorrect. Humans are not inately magic.
For example, a Divine character like the Paladin has zero to do with "gods". Even the Cleric derives the magic from a personal connection with the Astral Plane (playtest) via a "cosmic force" (Xanathars), including a philosophy.
My examples were examples only. Not a complete list of all sources of magic. Only sorcerers is innate. Paladins oaths. Clerics also from connection to something or someplace else. Not innate magic with no outside source.
Humans are innately magic.
You have not shown how at all. I disprove all your claims. You can play this way, but it is not the rule.