Thanks for the post! Currently, the ability to assign test cases is included with the permission to add results and comments to tests. Using TestRail’s existing settings, the only way to prevent a user from using the ‘Assign To’ functionality would be to remove that user’s access to add results and also comments to tests (this can be done under ‘Administration > Users & Roles’). However, I would assume preventing users from being able to add results isn’t the route you’d like to take.
We do have plans to review adding greater flexibility when it comes to access/permissions for a future TestRail update. I have added your vote to this feature request to help us prioritize this, however I wouldn’t be able to provide an ETA on additional permission settings at this time.