I do not believe that it is necessary to study science to be good at business, but I do believe that studying a broad range of subjects can be helpful to most people no matter what their career is going to be. In other words, I believe that studying science is helpful but not necessary.
In order to be successful in business, it helps to have a mind that is able to think creatively and to come up with different options in a variety of situations. There is no curriculum that teaches you how to deal with every eventuality that can arise in the business world. This, in my view, is where a well-rounded education comes into play. If you study the sciences, along with other subjects that are not directly related to business, you improve your overall mental abilities. You force yourself to think about things that you are not familiar with and may not be good at. You make yourself into a person who is more likely to have a flexible mind rather than a person who is very good at only one thing.
It is surely possible to succeed in business without ever taking science. However, I would argue that taking a variety of classes gives you the mental and intellectual skills that make you more likely to thrive in the business world.