As far as I am aware, Crystal wouldn't be able to access the CurrentUser information when you click on print. Crystal doesn't connect via TPS it goes directly to your database.
The only thing that I think would be possible is to have the different sets of users going to different WebAccess virtual directories (web access applications in config centre) and then each one could be configured to look for the reports in a different location. Each copy of the report can then be modified to suit the requirements.
It would make a good enhancement request to be able to improve this area of reporting: whether you could link a report name to a form design or via users/groups/roles as you suggested.