That's definitely wrong.
I can guarantee you, if the USCIS finds that you have registered a company on your F1, they will likely cancel your visa.
http://www.uscis.gov/portal/site/uscis/menuitem.eb1d4c2a3e5b...
Employment
F-1 students may not work off-campus during the first academic year, but may accept on-campus employment subject to certain conditions and restrictions. There are various programs available for F-1 students to seek off-campus employment, after the first academic year. F-1 students may engage in three types of off-campus employment, after they have studying for one academic year.
These three types of employment are:
Curricular Practical Training (CPT)
Optional Practical Training (OPT) (pre-completion or post-completion)
Science, Technology, Engineering, and Mathematics (STEM) Optional Practical Training Extension (OPT)
Optional Practical Training is for you to get a job in your field. That's it. Not start a company.
Edit: Ok...I take that back. You can't do it, if you want to stay in the good graces of USCIS and stay in the US. If you don't mind being deported...then you most definitely can. Nothing is stopping you - once you have an SSN.