I would imagine of they happen to be an S or C Corporations. I believe C-Corps are mandated to go public if they exceed 100 shareholders per SEC. It also depends.
> Companies with more than $10 million in assets whose securities are held by more than 500 owners must file annual and other periodic reports.
http://www.sec.gov/about/laws.shtml
The reason people believe that it forces companies to go public is because, in many cases, the incremental cost to going public (above and beyond the filing) is insignificant compared to the advantages.