> Black hole singularity is a surface not a point

Might they be trying to say this?

1. The boundary of the black hole which traps light, etc, is called the event horizon, and sits at the Schwarzschild radius. This is a geometric surface.

2. There is no singularity at this surface.

3. In models of black holes, there is a gravitational singularity at a point in the centre: https://en.wikipedia.org/wiki/Gravitational_singularity which is a topic with nuances.