Yes, in US anyone can start a company, but the catch is, you can't work for it without proper work authorization. So, practically, this means you can't start a company if you are going to take an active operating role within the company.
That's the law. The reason is, you can be a passive investor in a company, similar to buying stock in a company. This is allowed on any type of visa including H1B. But, if you are taking an active role, you are working for your own company and you cannot work for a company without work authorization. The work authorization could be CPT, OPT, EAD or H1B ( there might be other forms of work authorization I am only aware of these few).
