Dogs do not have the means to digest grass, as they lack the enzymes needed to break down the fibres. Thus, there is little nutritional value in it for them
Often it is a means to alleviate stomach issues. It can be becasue of gastric reflux (hiatus hernia in humans can cause this) It could equally be tying to alleviate gas - that can lead to bloat. That can be fatal
Why your vet psses this off without checking the dog is beyond me.