There are a very large number of different 'grasses,' around the World! In North America there is something like 20 types of grasses the vast majority of which would not harm a Parrot.
The Problem with the grasses found in the yards of North America is not the grass itself, but as stated above, its load of chemicals that are placed on or floats in from other yards and roadways around your specific lawn. Add to that the common load of less then great stuff that has been dropped and just plain exist in the grass and soil below.
In addition, in North America there has been a very successful return of the full cross section of the family of Hawks. With the Red Tail Hawk having the greatest success. A Parrot on the ground is an easy target.