Summary:

The hierarchy filtering feature, when enabled, can be used to limit users' visibility to departments, projects, and other users based on their placement within the organization's hierarchy.
Web TimeSheet Integration for QuickBooks tool does not have permission set or hierarchy filtering method as Web TimeSheet.
To be able to integrate, you would require Administrator permission in Web TimeSheet. Hence, the person who transfers data from TimeSheet to QuickBooks or vice versa will have access to all user data.