You don't need to be rich or even middle class to play music, but you're much more likely to get a flute and lessons on how to play it if you've got parents who aren't dirt fucking poor and/or totally uninterested in your education. Thus there's obvious an association between music lessons and family background that needs controlling for.

As for MJ, he might not have been born rich, but nobody would say his musical accomplishments weren't linked to decisions his parents made for him.