it has to be assumed since it's not impossible for charge to exist along the axes/points of symmetry for the conductor
i.e., a single point charge in the center of a sphere, or a continuous line of charge along the cylindrical axis of symmetry for a cylindrical conductor
there's probably some semantics about what the right 'definition' is
the formal definition i'd probably fall back on is "a conductor is what you get if you start with a dielectric material and take $\epsilon\to \infty$."