Let's assume humans are indeed "designed" to work in small groups of only 10 people, then at the bottom level of the company tree groups should only consist of 10 people each. So far so good.

But why has a company of 1000 a three-level tree structure with 10 groups of 10 groups of 10 each rather than a two-level structure with 100 groups of 10 each? You assert the reason is the 100 bosses couldn't work together as that group size would be too big. But the bosses don't form a "workgroup" in this sense anyway. They may meet occasionally but spend most of their time with their own groups. The reason for the additional tree level seems more that the supreme leader of the company wouldn't be able to oversee all 100 groups himself.

The distinction matters because for the purpose of being overseen, groups can be represented by their bosses without having to act as one person (as they might have to if their bosses formed a workgroup subject to size limitation due to humans' innate design), so the inverse relationship between freedom of the leaves and company size can't be deduced.