I have read that eating grass may be something of an "instinct" to dogs. When they used to kill and eat rabbits, birds, and such… they would eat the contents inside of their prey also. This gave the meat a wild, grassy taste and maybe that is what is lacking from the modern-day dog diet. NOT something easily replaced!!!
Have you noticed, (because I am wondering) do they take their time and chew it thoroughly when eating grass as a snack? I bet they do... that is why they don't throw up!
Most dogs (like Bella) will scarf grass down in a mad, hurried pace without hardly even chewing when they are sick. I don't know if the intention is to cause vomiting to occur, but think about all that grass (blades intact) tickling the insides of their esophagus and stomach!!! That would be enough to make me vomit!:p