Supports up to that many levels, but whether in Illy or Photoshop, I believe the gradients themselves are built using 256 fountain steps, essentially. So that's what's saved out in the EPS, whether Level 2 or 3 ... to my knowledge, anyway.
Seems you're right! Did some looking around, and nowhere does there seem to be an option for increasing the number of steps in an Illustrator gradient. Looks like nearly a decade later, the tail's still wagging the dog with Postscript 3. I'm sure it has its uses, but I'm not sure how to exploit it myself.
Only thing I did find was in regards to gradients made in Photoshop. Was in an old archived post here, and looked like Rooster mentioned saving from Photoshop as a 16-bit file. Nothing as elegant as an increase in steps of a vector though.
Even Adobe's help forum recommends 7 inches as the largest acceptable width for its vector gradients. I thought we were living in the future? What is this crap?