You’re misremembering. SM64 was fully textured, outside of specific models.

Also flat shading (vs. say gouraud shading) is isomorphic to the question of texture mapping, and concerns how lighting is calculated across the surface of the polygon. A polygon can be flat shaded and textured, flat shaded and untextured, smoothly shaded and textured, or smoothly shaded and untextured.

(Too late to edit but did not mean “isomorphic”, meant “orthogonal”. Wrong smart person word trying to look smart, how embarrassing, sigh.)