You can "graze" a rabbit, by putting it in a predator-proof pen, but this is
not practial for commercial rabbit raisers.  My sister has some pet rabbits
that she allows out in a home made pen and they love to hop around, munch on
fresh (no chemical) grass.  Then they lay down and relax.  It is important
that they are in the shade!  Rabbits can overheat quickly.
Rabbits tend to be quite lean.  As long as they are not being over fed they
don't have much fat.  Pet rabbits that are over fed can become obese, but most
people don't eat their kid's pet.  : )
Nicole
The Rabbit Guru