Kruskal-Wallis rank sum test output confusion
Your problem comes from using an incorrect test, the formula parameter says:


  a formula of the form response ~ group where response gives the data values and group a vector or factor of the corresponding groups.


When you apply the kruskal  test, you don't have groups in the LSC variables! You aren't comparing the mean of several groups based on LSC!
When you use stat_compare_means it is doing a wilcox.test (it hints to it in the help page "a list of additional arguments used for the test method. For example one might use method.args = list(alternative = "greater") for wilcoxon test.").

When you use the wilcox.test we get the same p-value:

wilcox.test(df1$HSC, df1$LSC)

    Wilcoxon rank sum test with continuity correction

data:  df1$HSC and df1$LSC
W = 110980, p-value = 4.849e-12
alternative hypothesis: true location shift is not equal to 0


In addition, probably you should read about the paired argument, if this two values where measured on the same samples you should use it (but I can't tell it for sure because I don't know what does it mean each variable name).