@ZayB As with all things "unreal", it depends on how the author wants to create the universe. You know, like how Batman is the best SIMPLY because he's Batman, when in reality everyone would kick his ass.
In this case, it's a bit like how "immortality" works, I guess. How do you define immortality? Not being able to die of old age? What about injuries? What if you get beheaded? You can't die, but you're not "invulnerable". Also, "eternal life" does not mean "eternal youth". You may continue aging, then grow old, your skin starts to rot and turns to dust... and you're a skeleton. Alive, but a skeleton.
A body that doesn't get ill still needs energy to function, which is essentialy what food is: fuel. Like, maybe he wouldn't get anemia from lack of nutrients, since we can count that as an illness, I guess, but the lack of energy in itself would render him immobile.