If your goal is to get shredded, should you have carbs on off days? Here's what a lot of bodybuilders do.
This is a pretty common approach in physique sports. Matt Porter, for example, one of the smartest men in bodybuilding, uses this approach during contest preps. And it's been around. Thirty years ago the late Dr. Fred Hatfield, who squatted 1014 pounds at age 45, wrote, "Eat for what you're going to be doing and not for what you've done."
If you aren't going to train hard, and your goal is fat loss, then you don't need "fast fuel" that day. Note that if your goal is to build maximum size, not get lean, I recommend having carbs on off days. But when trying to get lean this is a very simple approach. You don't even need to necessarily count calories, just don't eat any carbs.
Should you increase fats to compensate? No. If it turns out that you eat a bit more fat because you have more steak that's fine. But don't add fat sources on purpose. You won't turn catabolic in one day! This will provide a nice caloric restriction when it will have the least negative impact on your training performance and muscle building.
I do believe that carbs are very important when trying to build and preserve muscle mass. Carbs give you more fuel in the gym (better performance equals better gains), help you recover after your workouts, and increase IGF-1 and insulin levels, which are very important for muscle growth if increased at the right time.