That's true in a way. I think of grinding as in you have to go over a level many many times to get strong enough to get past (obstacle).
In Diablo, just playing through a level once gets you strong enough to move on. If you want special items for special purposes you'll have to farm a level sometimes. In order to get to the unicorn level you do have to go after specific items, but its not required to get through the game. So, if you do grind, it must be for your own benefit, you certainly don't need to in order to get through the game.