It's always a bit dangerous to speculate on someone else's reasoning, but suspect something like this:
PART I: Blood glucose must be maintained (since the nervous system depends on glucose for energy - the brain does not use fats like muscle can). In a carb depleted state, the body maintains blood glucose by synthesizing it from other substrates (gluconeogenesis). Some of the major substrates used for this are amino acids (the major building blocks of proteins). So, with low carbs, a lot of the protein will be used in gluconeogenesis. This does not mean that the protein is wasted, but carbs are generally a lot cheaper than protein, so why use the protein for gluconeogenesis? Plus, in gluconeogenesis from amino acids, the nitrogen from the amino acids ends up having to be processed to urea and eliminated.
PART II: Carbs have a MUCH stronger effect on increasing insulin than protein alone (protein alone gives some increase, but also increases glucagon at the same time). Insulin dramatically increases uptake of glucose by muscle, but also increases amino acid uptake by muscle tissue, and increases protein synthesis. This could also be part of the reasoning. This is more likely to be a factor in formulating a post-workout recovery drink.
SUMMARY: It's not complete bunk. The carbs could make protein utilization more efficient, depending on when it is consumed and the rest of your diet. But without carbs, you would still utilize the protein, just some would be used to synthesize glucose if carb intake is too low.
