As I said, concepts like "point" and "contact" are murky on the level of atoms and molecules, so there really is no "right" physical answer. I merely went with the geometrical picture that comes the closest to a "point" that still makes any sense on the atomic level. And that's a picture where one atom of one surface balances in a hole formed by an elementary cell of the other surface.
There are other possible answers. One could be rigorous about it and say: "Ill-specified problem: There are no ideal geometrical bodies in physics."
Or one could define "contact" in the spirit of your objection. For example, one could say that "contact" means that the distance between the surfaces is smaller than the length of a chemical bond within them. That gives you a "point" of contact that grows with the size of the sphere.
Based on trigonometry and the back of an envelope, I'm getting a radius for this "point" of contact that's sqrt(2 * r * g), where r is the radius of the sphere and g is the size of the gap. For example, if r=5cm (for a grapefruit-sized sphere) and g=250pm (which is the length of one Fe-Fe bond) the area of contact would be a circle with a radius of 5 micrometers. And as you suggest, the area grows as r grows.