Currently, (as referenced from James C. Williams at Blackbaud) complist page is displayed based on a calculation table.  Each type of item in a Teamraiser has a unique table where this data is stored: participants, teams, and companies.  Each Teamraiser has their own set of data.  Copying an event does not copy the stats between the events.  So for the complist to display a company an item would have needed to be connected to the company in some way for the UpdateTeamRaiserStats task to perform a calculation and roll the data into the company data table.  Once it is in the table then it would be rendered on the complist page.  Lists for Teams and Participants behave in a similar way and require them to be created and pulled in through a list through the stats task. 

So until the UpdateTeamraiserStats task recognize that the company serves a roll for this event then it would not be pulled into the company stats calculation or the complist page.  This task runs every 15 minutes, so once something is connected to the company in a way for the stats to be calculated then it should show up shortly after.

As it stands, if you credit an event gift to a national company and let the stats task run that it would be pulled into the complist page.  If you subsequently delete the gift then the company would remain.  So the only apparent workaround to get this to display companies without it just naturally populating would be to connect offline gifts then remove then so they will be created in the database.

It would be preferable if this was automatic when copying events :)