You've been talking to some real dumbasses then
Why? I don't think it meets all the criteria (hell I'll freely admit I'm not 100% sure what all the criteria to call a state fascist would even be), but it meets a great many. As in:
Supreme leader idolized to the point of a personality cult: Check
Means of production remain largely in private hands: Check
Criticism of the state and its leader dealt with harshly: Check
Fails:
Idolization of the military/Military ideals: So far as I know, no
Some bizarre fetishization of an idealized past: Probably not, but Lee did push some sort of neo-Confucianism, IIRC
Note that stuff like racial purity isn't inherent to fascism. It wasn't a factor for the first decade of fascism in Italy (there were even Jewish fascists elected to Parliament at one point, Mussolini essentially did a complete about-face on this) , and never was in places like Spain under Franco and Portugal under Salazar. It was in Hungary, but only after Horthy was overthrown in 1944 and the Arrow Cross loons came to power. Croatia was basically doing what they always do: hating Serbs, not sure how racial they got beyond that.
The inevitability of territorial expansion pushed by National Socialism, Italian fascism and Japan under Tojo is also unique to those regimes. They were certainly the three largest regimes, but I think you'd be hard-pressed to say that this is a fundamental characteristic of whatever it is you'd call fascism.