So you'd be ashamed to be in grad school? (Or doing a startup right out of college?)
Often the insurance offered by a parent's plan blows away what can be had through the University. Of course, you can buy individual insurance fairly cheaply... unless you aren't in perfect health, or are a girl.
Last year I finished my graduate degree in computer science. I worked a full-time job while doing that (also during undergrad). I'm actually pretty proud of it. I finished up grad school with a lot of work experience, zero debt and had insurance the entire time.
I'm currently a CS grad student, with zero debt, working as a GTA/GRA (depending on the semester). I get my insurance through the University for an awesome $94 a semester, but if I were still young enough, I'd definitely opt for my parents insurance, and I wouldn't be ashamed of it. It would just make financial sense.
Not everyone would be able to do this though. Working more than part time I'd feel that I couldn't put enough time into my education. I know some people are better at quickly being able to switch tasks and work effectively in short blocks but not all.
The insurance offered through my university was certainly terrible. It was very cheap, but there was a reason for that - it provided as little as possible, and made using it as difficult as possible in the hopes you'd just give up and never use it. Being on my parents' plan would've been night and day.