Is it just with relief texture? Sounds like they are 3d scanning and printing with the exact same texture. And if that's the case, it doesn't seem that hand stretched canvas would matter.
Sufficient resolution and materials with identical color and refractive qualities should get you a visually identical result.
Consider 3D reproductions of plates of food in restaurant displays. Can they really look edible? What level of texture would be "sufficient" in that case?
Food is made of many different elements, all of which have different reflective qualities. A 3D printed gravy-soaked chicken and salad, in far finer detail than is currently achievable, would still look fake, even from a distance. In many cases, oil paintings are made from paints with near-uniform reflective properties, which would work far better, assuming that such properties could be reproduced in some special-purpose 3D printing material.
Sufficient resolution and materials with identical color and refractive qualities should get you a visually identical result.