Hi Cutterchoice,
I would suggest the following solution:
Add your user (or groups of users who are meant for this job) to a Security Role which has Activity Read permission as User. Then once the Agent assigns a particular call (I believe you're referencing to Phone Call) to a particular user (among
those in the Security Role), the Phone Call activity will only be visible to that User and no other user (in that Security Role).
But users who are System Administrators or are assigned to Security Roles which have Activity Read permission as Organisation would still be able to see all Phone Calls.
Admin QuikView Solution for CRM 2013