Add Folder Security to Groups
In order to prevent a user from responding to a ticket with the same ticket number as another area, add folder to security to the group. When the folder is selected in the group, only users in that group can respond to the ticket.
I agree with enabling folder access based on group membership as this would greatly simplify user administration/access provisioning of new users. As the workforce changes there is constant work by an administrator role and lots of documentation required to ensure you get all the screens and filters and folder access and notifications set up for that particular user. Then if they move to a new area or move to a supervisory position....it is a whole bunch more work.
A slight variation of this idea (if you wanted to keep groups to be more permission based) would be to add users to a a "Work Queue" type of object. Then folder access would be granted to all users in the "Work Queue". Notifications and alerts could also be sent to the "Work Queue". The existing "Group" could function/be used the same as a "work queue" if adding the new item is too complicated.