This is purely based on the definition of "density" here, which is the mass of the black hole divided by the volume inside the event horizon (which is the invisible/black sphere).

However the event horizon does not represent the extent of the mass of the black hole, but rather the point where gravity becomes so strong that nothing can escape it, even light (hence "black" hole/sphere).

We don't really know what's inside the event horizon or how the mass if actually distributed. The concept of singularity is that all the mass is located in a zero volume with infinite density.

> We don't really know what's inside the event horizon or how the mass if actually distributed.

Is that entirely true? We can tell if the black hole is rotating because of the frame dragging that happens outside the event horizon. Could we tell anything about the radial distribution of mass from the shape of space outside the event horizon? (I'm asking; I don't know enough GR to know.)

Well we do reasonably know that the mass must be very densely packed at the centre but we do not know exactly how, we do not know if there is a singularity or not.

If a rotating black hole was not just a point, if it had a radial distribution, would the frame dragging be different? Could we tell that way?

just like most fat people have lower density than skinny ones