but he'll still happily eat a few pieces of meat or some of his dog food if I offer it to him.
No. Have you ever seen a dog grazing in a wheat field?
I give mine whole wheat buns from the mark down bin.
I never give my dog any people food and never any grains in his own food or treats
It's not going to kill him, but it's not good for him.
No.
It's best to give him whole wheat or whole grain bread. White bread has too much sugar.