By that logic neutron stars should be black holes. But they're not.
Neutron stars are in a sense "failed" black holes because of not enough mass. I wonder if they could eat more mass and achieve that status though.
https://news.ycombinator.com/item?id=7104056
Basically it's unknown if it is a two star system where the neutron consumes the partner, or a three star system where two neutron stars collide head on.
http://en.wikipedia.org/wiki/Tolman–Oppenheimer–Volkoff_limi...