Well, being a competitor myself, I can tell you that not everyone diets for a show with severely low carbs. Also, BB's (if they're smart) still eat some fats.
Some go the ketogenic route, low carbs, higher fats and proteins. Some do minimal fats and higher carbs with moderate proteins. Some do carb cycling. It varies person to person, just like it does with non competitive lifters.
Obviously, a main goal for a competitor during a cut, is preserving muscle mass. That's why I say that if a BB is smart, they won't go drastically low on their carbs too early in their diet. The keto diets, which are pretty darn low carb, aren't the best for long term muscle preservation.
Personally, I do what could be considered a kind of carb cycling. My lifting days I have moderate carbs, cardio days are minimal carbs, with a once or twice a week refeed.
But overall, IMO, the reason that competitve BB's 'seem' to be able to shed fat in such a short period of time (on average 12 weeks) is because the competitors are much more precise with their calorie tracking than those that aren't competitive. IME, the people that are just 'lifters,' when they're cutting they just make a conscious effort to eat a little less as time to goes on. They estimate their portions and have more of a 'that looks close enough' attitude. Whereas when a competitor has a show coming up, every little thing gets weighed and tracked that goes into their bodies. Heck, I even weigh my peanut butter. So being that a competitor has a set date where they have to look their best, there's much more accuracy in tracking everything they do with their diet.
But that's just my take on that.