You can't cut carbs without losing muscle. That's just not physically possible. You lose _some_ muscle inevitably. Every single book or study on sports nutrition will tell you that. The best environment for growth ("bulking phase" in bodybuilder terminology) is when you have significant caloric surplus, and increased body fat in 15%+ range.
Let's consider an example. Take a strong 220lb male athlete. His daily protein intake should be about 200-220 grams. That's only 880 calories at the upper end of the range. You still need at least 2500 if the guy is undergoing intensive training. You don't want to be eating too much fat. Let's say you consume 90g of fat per day (that's roughly in line with recommendations). That's another 810 calories. Mmmmkay, you still need 1690 calories. And that just happens to be a tiny bit over your 400g of daily recommended carb intake. So there you go. And this is not what I'd call an "excessive" diet for someone who trains and wants to actually see any kind of a result. I'm heavier, and I eat proportionally more than that. To "cut", this athlete will have to eat a bit more fat and significantly less carbs to create a small caloric deficit wrt his daily nutritional needs without becoming too catabolic. He will do that for 4-6 weeks after which his metabolism will begin to slow and he will have to start bringing in carbs into his diet again through "reverse dieting". If further weight loss is needed, the athlete will then undergo another "cut" cycle, _after_ metabolism returns back to normal.
Now granted, this is for someone who trains a lot, given to a sedentary adult this diet will result in massive amounts of fat gain. Adjusting it is just a matter of scaling these numbers down to the desired calorie intake (as well as taking up exercise to boost the basal metabolic rate).
Trouble with most athletes is they _think_ they don't eat a lot of carbs or fat, but unless you pre-make your meals with a scale and a spreadsheet, there's just no way to know how much of each macronutrient you're eating. That's what I do, anyway, it works for me.
Besides, even if your trainees really do cut carbs on their "off" days, they're still eating a ton. It's difficult to consume 200+ grams of protein per day, especially if you try to do so via food and not protein powder.