It does not mention in this article whether the graphite is flake or hydrothermal. That would stand to make a huge difference in costs of purification.

It also doesn't say what % graphite the flotation sample was to start, again making a huge difference.

The chemical treatment in your example employs sulphuric acid, therefore not being a caustic bake.

And how you draw the conclusion that Oliver Peters thinks chemical is cheaper than thermal from that interview is a mystery to me. The interview continually leads him on to agree with that fact, but he never states it outright, merely acknowledging that either could work for any given sample of graphite.

Given the extremely high concentrations that the other graphite company begins with by simple flotation, I can't see how heating would be very expensive at all. And as John Hykawy pointed out, hydrothermal graphite was formed in high heat conditions, so thermal upgrading should be fairly benign for lump graphite. But we'll see, I guess.