When using the command with symbolic parameters for a normal distribution
KolmogorovSmirnovTest[data, NormalDistribution[\[Mu], \[Sigma]], "TestData"]
you are testing whether the data comes from a normal distribution. That is the Lilliefors Test and it has a different P-value calculation. See https://en.wikipedia.org/wiki/Lilliefors_test.
When you want to test against a specific distribution with specified parameters such as
KolmogorovSmirnovTest[data, NormalDistribution[0, 1], "TestData"]
then the formula for the P-value works.