Your example doesn't apply, as special relativity does not allow light-speed travel. (The FTL travel of the article involves stretching distances behind the traveler, so zero separation again does not apply.)
One could point out that near-light-speed travel would bring the stars into arbitrarily close proximity. But many other observations would also change, e.g, the shape of the stars; if one works out ALL the physics, no laws are violated in the traveler's frame of reference.
“Your example doesn’t apply, as special relativity does not allow light-speed travel.”
Of course it does. Zillions of photons are traveling at the speed of light right now, perfectly in accordance with special relativity. It just doesn’t allow you to accelerate a massive object to the speed of light (in the spatial dimensions).
“if one works out ALL the physics, no laws are violated in the traveler’s frame of reference”
Which is not the same as saying that their perspective, in their frame of reference is as accurate depiction of objective reality as every other. The math may work perfectly well, but the conclusions you draw may not be the correct ones, if your perception of reality has been skewed, for example by the relativistic effects that I’ve already mentioned.