I don't think that's true. I'm currently on a diet that's fairly high in protein (and to go with the theme of the article, comes out to $4-$6 a day I believe). I don't think it's barf-worthy.

Example: Breakfast: Scrambled eggs with a little salsa on top, bacon, mixed veggies Lunch: Usually salad of romaine, spinach, mixed greens, cucumbers, tomatoes, cheese, grilled chicken, and homemade dressing. Sometimes I'll have chili instead of a salad. Dinner: Usually a pork chop or chicken breast, some spiced lentils, and mixed veggies

I think that's a pretty well balanced high protein diet. I'd estimate it as 60% protein/20% fat/20% carbs. The veggies add relatively few carbs. The only thing it's really "missing" is starchy carbs. Sure, if your high protein plan was 2 pounds of beef a day, I'd go and say it's barf-worthy, but I'd argue most low-carb diets aren't.