In the example of a spaceship moving from earth to whatever star at a good fraction of the speed of light, we have two main frames in which to view the situation. Either we take the frame of the spaceship and we'll indeed see a squashed star. Jeff seems to prefer the other frame (the earth-star system) in which the star is spherical but then of course the spaceship is squashed. So as far as i am following his argument, he seems to be stating that he prefers to consider squashed spaceships over squashed stars. Though i have no idea why he prefers that, it is his right to prefer to view things that way. As long as he doesn't argue against any of the physical results i don't really see the problem.
I do have a question for Jeff Root though. Suppose that instead of a spaceship we hurl a star towards another star. Then in every frame at least one of the stars is going to be squashed to at least some degree. Which frame would you then prefer and why?