Maybe that should have been “you may go low while drinking” and then either (as you point out) be too impaired to deal with it, or be exhibiting symptoms of a low (slurring, difficulty focusing) but those around you just assume you’re drunk.
Anyway, I heard the same advice when I was younger. I prefer to eat something when I’m drinking not to avoid going low, but because the food can slow the absorption of the alcohol so I’m not blotto in ten minutes, and also because the two can play off each other so well, just like wine can enhance food and vice versa. Cheese straws and salted nuts were invented for a reason.