Yes, running on the road is illegal. It's not obvious what your friend was referring to, but I can think of two likely options:
1) Elk Park, as Mark mentioned. It starts at almost 12k ft, just below treeline, goes 5.5 miles slightly downhill to Barr Camp, and from there you can take Barr Trail to the summit. One-way, it's about 11 miles, including 1500 ft of elevation loss and 4000 ft of elevation gain. The parking lot is hard to find, I can probably post an image if this is what you're interested in.
2) There's a large parking lot at Devil's Playground, at almost 13k ft. From there, you can get on the Crags trail to the summit, which parallels the road for a while.
I'm not aware of any spot along the road lower down that's runnable to the summit.