I think you and Dr. Brain are saying the same thing. The Schwarzschild radius for any (spherically symmetric) massive object can be calculated. If the the Schwarzschild radius lies within the object (i.e., the object has mass outside), then the object is not a black hole; if all the mass lies inside its Schwarzschild radius, then the object is a black hole. By Birkhoff's theorem, a distant observer cannot use gravity to tell the difference between equal mass (spherically symmetric) objects, be they stars, black holes, or even stars collapsing (spherically symmetrically) to form black holes.
Regards,
George