I'm sorry to repost on this 1 1/2 months later, but 2 different people from QuickBooks don't understand a very simple question. This shows if you can't even follow the OP's question, how could you possibly attempt to solve these issues?

Your solutions is to uninstall and reinstall?!?!?

I'm sorry, but this is unacceptable 'support' and it prevents people with an actual understanding of the software from answering the question.

I found myself here to piggyback on the OP's question finding ourselves in a similar position - 

1) Is there a file, such as a .ini or something else, that stores the information/list of recently opened QuickBooks company files, 

2) is it possible this information is stored in the registry?

In an Enterprise environment, it is unreasonable to have your software be such that administrators only way to change this information when changing servers, file shares, etc., is to open the company file in the new location by signing in under the context of the current user's profile.

To Intuit - invest a little time and research into finding these types of COMMON problems and put solutions to these into your releases. Also, invest a little time into proper technical training of your staff that you are assigning to answer these community questions. There are thousands of examples here in your community of problems that could be solved by your staff that nearly are always solved by other community members, members without a QuickBooks title.