There has been talk on other questions of how one might use the Two One-Sided Tests (TOST) approach for the Kolmogorov-Smirnov (KS) test, but I was wondering whether it was possible to directly use the test statistic to show that two distributions were similar?
As far as I understand it, the KS test statistic represents the biggest difference between two CDFs, with the one-sample version being used originally as a goodness-of-fit test. This is shown in  as being when the empirical distribution crosses outside the confidence interval (i.e. any one point is too far from the hypothetical distribution they are testing against).
If the two-sample version is often used to show that two distributions are significantly different to one-another, in a similar way to the one-sample version, can we invert the calculation of the confidence intervals from using $(1-\alpha) = 0.05$ to instead use $(1-\alpha) = 0.95$, as a way of showing that the maximum difference between the two distributions is significantly similar?
 Massey, F. "The Kolmogorov-Smirnov test for goodness-of-fit", Journal of the American Statistical Association, vol. 46, no. 253, pp. 68-78, Mar 1951