Simply put, a Kolmogorov-Smirnov test realizes a method, but interpreting it as proof is a dangerous oversimplification.
The test identifies a statistical similarity, end of story.
If the input data are flawed, such as unadjusted venture capital returns for capital controls, the test only validates an initial bias.
Robustness comes from the intrinsic quality of inputs, not the tool itself, as constantly reminded by the BRI.