It's not really that cut and dry. The point is more that you need to keep your protein levels high when cutting to reduce muscle loss... and the only (good) way to do that on a restricted calorie intake is by reducing carbs.
Simplest example, if you're working with 3000kcal and are aiming for 150g of protein (calculated by body mass) then you have 2400 kcal for carbs and fat. If you're working with 2000kcal then you only have 1400kcal for carbs and fat. Something's gotta give... and it's usually best to make it carbs. That's one of the reasons people change their macros for cutting (or go full keto). Many people actually increase their protein intake too, but I'm yet to see conclusive science that supports that methodology (ignoring those on fairly low protein intake when bulking).
Unrelated, have leg, back, shoulder, neck and arm DOMS. Only thing not aching right now is my stomach. Really don't want to work out tonight but it's grin and bare it for back day then a rest day tomorrow.