The correct answer would be: No. All plants obtain most materials for growth from water and carbon dioxide.
While it is true that the tree is larger and typically can access more sunlight due to its height, the amount of materials a plant uses for growth primarily comes from carbon dioxide absorbed from the air and water taken up through its roots from the soil. Both tree and grass obtain nutrients, but the fundamental reason for the size difference is more complex than just proximity to sunlight or the amount of materials taken in.