If the law of physics that determines maximum density of matter is broken during the initial creation of a black hole, then shouldn't all laws of physics be invalidated within the event horizon (Schwarzschild radius) of a black hole?
Several laws of physics as we know them don't work inside a black hole.
Black holes were first predicted by the Schwarzschild solution to the General Theory of Relativity. As not even light can escape the event horizon of a black hole, then we can never see inside one. Our laws of physics as we know then can't describe the inside of a black hole.
Our physics predicts that there is a singularity inside a black hole. This is a point of infinite curvature of space time and infinite density. Whenever an infinity appears in mathematics or physics we need to change the theories to eliminate the infinity. General Relativity fails at the singularity.
There is also the information paradox. If something falls into a black hole and information about its state is lost this is not allowed by the laws of physics as we know them. Stephen Hawking is working on a theory to resolve this whereby the information is stored in the event horizon.
We know black holes exist, but our laws of physics as we know then simply can't describe them.