“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.
Barking nonsense; math is the language of physics, so if the math works then the physics applies.