Is this particular point so terrible? I'm 23 and am still on my parents' plan. The marginal cost of keeping me on their family plan is so much less than the cost of me getting my own line that it makes little sense for me to get my own, even though I could easily afford it.
In the context of the article, it reinforces the idea that he's spoiled - that while his parents continue to pay all of his bills, he turns down what most of us would consider a more than reasonable starting salary given this economy, his major, and his lack of experience.
I would assume that in your case (since you could easily afford your own line), you're at least reimbursing your parents. This guy isn't.