Given the very limited readout of "skills", how could it be otherwise? Nothing in their measurements captures the actual skills taught by music lessons (piano-playing ability, music appreciation, etc).

Perhaps music lessons have some second-order effect on "does neat, careful work", but it doesn't seem impossible that might have opposing effects on other so-called skills too: "too fearful or anxious" for stage fright, "disobedient" for not practicing when told.