Are you sure that quote isn't referring to the length dilation that occurs in a gravity well? Space is non-Euclidean so you can have a sphere with a radius larger than the circumference would allow.
His quote is exactly referring to that: but my question is, are black holes curved enough that you can have a circumference at quantum scale with a diameter above that scale? — ie, at which quantum effects would happen around but not across the singularity.