He didn't say "the speed of light in a vacuum", he just said "the speed of light". And in the next sentence he said
> … it is simply not possible for light to be still, or even propagate at a different speed in the same medium.
So he's already acknowledged the fact that the speed of light depends on the medium. His point, though, is that light must still travel at this speed (even though the speed itself depends on the medium).
The speed of light in a medium is still the speed of light in vacuum if you look carefully enough. The apparent slowdown is just an emergent effect due to the interaction of photons and the particles making up the medium.
> … it is simply not possible for light to be still, or even propagate at a different speed in the same medium.
So he's already acknowledged the fact that the speed of light depends on the medium. His point, though, is that light must still travel at this speed (even though the speed itself depends on the medium).