Depending on your reference coordinate system, space is transformed. That is the entire point of relativity theory. You might be misunderstanding things here.
You seem to be of the same opinion as Sabine when it comes down to distinguishing between mathematical modelling, and reality. In mathematics though, coordinate transformation and space transformation are the same thing. How that plays out for the actual physics happening, might be a different thing, but note that you still describe it mathematically.
