No, that's not really what I'm saying. A black hole is a just a region that light can't escape from. It is entirely possible for the inside of the black hole to be composed of normal, everyday matter, non-singularity matter. The Schwartzchild radius scales linearly with mass, an unusual relationship that means that for any density the O(r^3) volume will eventually be overtaken by the O(r) Schwartzchild radius.