Actually here are the real numbers. GP is pretty close, though.
It lumps all accidents together, I couldn't find a breakdown of them. But I am willing to be that car accidents are the vast majority of them.
1. Accidents (over 37% of all deaths in this range)
5. Heart Disease
(HIV is #6 for the 25-34 group)
Cancer and Heart Disease are #1 and #2 overall. Those will tend to get almost everyone in the end. If you manage not to die young.
Now, comparing with the 2002 data, a large drop in accident deaths in the 15-24 group, while 25-34 group went up. The total for both groups is lower, though. I am going to go out on a limb here and say this is due to cars getting safer, and not teenagers getting smarter.