Right. They were labeled as martial so there is no way anyone could possibly consider them spells with a different label.
No one speaking in the context of the game could call exploits 'spells' without being objectively wrong, yes, because they would be saying something explicitly contradicted by the facts.
'Martial' was not just a fluff label but a keyword, so whether a power was an exploit or a spell had real meaning within the game. How powers, feats & items interacted, for instance, could hinge on what the source keyword was.
Not only that, but while all classes received powers in comparable numbers and of similar effectiveness, certain sources tended strongly in some directions rather than others. The most dramatically (in keeping with D&D tradition, ironically), were Martial and Arcane, and, specifically Fighter & Wizard. The former did not simply use the same powers labeled 'exploit,' instead of 'spell' and attacking using STR instead of INT. The differences go much deeper than that. All fighter attacks have the Weapon keyword, all wizard attacks use Implements. The rules for implements & weapons are distinct. 'Casting' - vocalizing & using gestures - is an aspect of using an implement power, but not a weapon power, for instance. Dispel Magic, a classic spell, is on the wizard list, and it keys off Zone & Conjuration keywords - something no Fighter power actually has, for another example. So saying "fighters cast spells" is objectively wrong on more than just the factual label of the martial & arcane keywords and the jargon meaning of 'spell,' it is also quite wrong on the mechanical and narrative levels.
Having a "martial power" that let me automatically distract everyone in the room so that I could waltz past them without provoking attacks wasn't magical at all. No-sirree.
You see a bad-ass action hero zip through a crowd of foes, often cutting them down as he goes, all the time. It's positively cliché in
chambara, for just one instance, and hardly out of place in fantasy. Nothing magical about it, except maybe the metaphorical movie magic of camera angles, editing, and stunt men.
So your sarcasm is misplaced.
I'd call them supernatural, but of course the text of the books may not have called them that so I'd be "factually wrong" about that opinion as well.
Dropping 'IMHO' at the end of a false statement doesn't make it true. "The World is Flat, IMHO," says the flat-earther, but the world's still round. So, yes, you are making as false a statement as the flat-earther or the holocaust denier. Whether your are deluded, trolling, confused, misremembering, inadvertently presenting an opinion in metaphor as if it were a statement of fact, or lying I can't tell - I will, of course, because we are being polite, here, assume the least offensive possibility. But, I'm sorry, I cannot, with any amount of respectful politeness, assume that a false statement is true. Instead, I would encourage you to correct your misapprehensions and stop making false statements (or resorting to poorly assembled metaphors with the appearance thereof), and simply state your opinions in a clearer way.