I never said the most probable distance
was zero. The most probable distance is indeed the Bohr radius, and the most probable point is r=0. These quantities have different dimensions; the radial wave function and its square has the dimension of a 3d point - an infinitesimal volume element. The radial probability distribution, which you're referring to, is one-dimensional quantity - an infinitesimal line segment.
What's so difficult to grasp about this? If I paint a set of spheres with an amount of paint that's exp(-r) per area unit (and somehow infinitely thin regardless of amount), then the point
that has the greatest amount of paint isn't the same thing as the sphere that has the maximum amount of paint on it.