I take the other view. I am not, and have no wish to be, an expert on torture instruments, but I don't remember reading references to drilling holes in people as a medieval torture, though no doubt it would be painful. And a drilling brace alone is no use for that without a drill bit. We had one of these at home when I was a child; my father called it a brace and bit. "Brace" alone in that sense seems to me an unlikely item to mention, compared to the others (racks, pincers and flames).

I think it refers to your other suggestion, a metal device for holding someone in an uncomfortable position that gradually becomes intolerably agonising. One such instrument was the cicogna ("stork" in English), apparently devised and used by the Roman Inquisition; there are illustrations of this online. A variant, devised in the reign of Henry VIII, was the "scavenger's daughter" or "iron brace", used in the Tower of London. Henry VIII himself owned one, it seems; it's described as an "A-shaped iron brace, inside of which a victim would be made to sit in a crouched position, with their head almost touching their knees, and their wrists, ankles, and neck shackled in place".
http://mentalfloss.com/article/64629/9-bizarre-objects-owned...

It's the opposite to the rack, in a sense: instead of stretching the body, it compresses it.

There are also neck braces described in some places, with spikes inside. Urgh.

I find this kind of thing very unpleasant and don't want to cite any more references. But I would say that a device of this kind is most likely to be what your text is referring to.