Running a KS test is only a mechanism, not a proof in itself of the validity of an interpretation.
The simplest is to understand that the relevance of a distribution test depends on the input data, not on the mechanics of the test.
If the data are biased or incomplete, like manipulated market data, then the KS test is useless.
For example, a statistical similarity in currency distributions is worthless if it ignores the interventions of the MAS.