What muscle are you suggesting that picture is implying one should inject into?
Im 100% sure it's not the lower back. You can see the crease where the oblique starts (or ends, I forget)
I mean, its called the dorsogluteal site. Not the "middle of the glutues maximus site".
The injection goes near the top of the gluteus maximus, near the gluteus minimus.
Logically, every text book cant be wrong.