This is only true if management respects the estimates. In my experience, they do not understand why Fibonacci or t-shirt sizing, etc. are used. They mentally convert the points to some "X days" and then beat you in the head with it. They want to micromanage and they do not understand they are building software. You can't break certain tasks down further and you can't parallelize many tasks. You can bring up Fred Brooks but it's a hopeless cause. They will never get it. Then as you inch towards their arbitrary deadline (that they tell no one, by the way, because it's better the developers don't know about deadlines until the last fucking minute because "agile" and not "waterfall") they suddenly act shocked that 9 women really can't make a baby in one month.
But I digress.