After a little more investigation, Nick and I have found out the problem. Because the Recorder CD used was not the latest, it had put all the installation folders under c:\program files. For compatibility with Vista and Windows 7, Recorder should really install the folders which contain any files that might change under c:\ProgramData, including the map files and object sheets folders used by the mapping system when you setup maps and add layers. Because they were still under c:\program files, Windows 7 will deny access (unless of course you turn off user account control).

Here is the list of steps we defined to fix the problem:
1) Close Recorder, then create a folder under c:\ProgramData\ called Recorder 6.
2) Move the c:\Program Files\Recorder 6\Map Files directory to c:\ProgramData\Recorder 6
3) Move the c:\Program Files\Recorder 6\Object Sheet directory to c:\ProgramData\Recorder 6
4) From the Start Menu, type regedit into the search box, then run the application regedit.exe. You will be asked to confirm the operation by Windows since this is an administrator tool.
5) Before going on, please do NOT change anything in regedit other than exactly what is described here. There is potential to do damage!
6) In the hierarchy on the left, browse to Computer\HKEY_CURRENT_USER\Software\Dorset Software\Recorder 6\Settings.
7) In the list on the right, double click on Map File Path. In the popup box, change the Value data box from its current setting to C:\ProgramData\Recorder 6\Map Files\ (including the trailing slash) then press Ok.
8) In the list on the right, double click on Object Sheet File Path. In the popup box, change the Value data box from its current setting to C:\ProgramData\Recorder 6\Object Sheet\ (including the trailing slash) then press Ok.