They are generally self-employed consultants as I understand it. Certainly a few guys at my airline are "BA checked" and teach BA pilots at CTC. I flew with one a few weeks ago who said they are also required to go through a standards check with a BA trainer before being let loose at CTC, presumably to avoid situations like EMB describes.
Icanseecearly: Good for you, I would have walked out too - far too many people are putting up with sub-standard instruction at CTC.