He wasn't born a celebrity millionaire. He dropped out of college (scholarship, and his mother was a professor there who didn't approve) to pursuit a career in music, took him a decade to break out.
The interesting thing though about most successful rappers is that, while almost all of them come from poverty, they tend to achieve success early in life such that by the time they hit middle age they've been rich longer than they've been poor (Nas notes this in one of his songs)...
A guy like Jay-Z talking about hardship increasingly sounds out of touch :)
Edit: Wikipedia says, "middle class" and the college he dropped out of was an art school so it isn't like he was giving up a sure thing to take a course that was more risky.
I don't buy the premise that you need to be poor to have an appreciation of risk. Risk isn't just financial, there is also career and personal risk. Think of all the well-off kids who didn't follow in their fathers footsteps or what their parents wanted and pursued their own dreams, at the risk of being alienated, disowned etc.
Knowing what college professor's salaries are like, "at least upper middle class" is way optimistic, though "probably solidly middle class" is likely.