I'm guessing the 13km diameter refers to the event horizon rather than the singularity itself, which I gather could be considered as zero-sized, or maybe one Planck length in size because we can't definitively measure anything smaller, or ...

Admittedly, it gets a bit philosophical. The sphere of no return isn't the thing, but it might as well be for any outside observer, but it isn't, but it could be viewed as such, but... :) Suffice to say I'm glad the closest thing to black holes I have to contend with in my daily life is a 2+ million line php codebase dating from the late Clinton administration.