Exactly. My total wealth on graduating from law school consisted of a used car, one shotgun, an electric typewriter, and a modest wardrobe, plus a $700 (that’s right, seven hundred dollars; it was 1967) student loan debt. Much of the wealth I’ve acculmulated over the years has been by saving from muy earnings. Race had little, if anything, to do with that.
From the author's point of view, you still have benefited from your parents' (and previous generation's) accumulated wealth.
Even though you started out on your own, the 'safety net' was still there.