You are correct! This is how I understand it as well....
A Sales person is first given the Sales person PRIVILEGE. Then define the ACCESS LEVEL for that privilege for EACH sales person. Either Global, Deep, Local, Basic or None.
A Territory manager would get an access level of LOCAL to see ALL records. A Sales person would get an access level of BASIC to see their own records only.
BASIC = This access level gives a user access to records that the user owns, objects shared with the user, and objects shared with a team that the user is a member of. This level is the typical level of access for sales and service representatives. The application refers to this access level as user.
LOCAL = This access level gives a user access to records in the user's business unit. Users who have local access have basic access automatically. Because this access level gives access to information throughout the business unit, restrict it to match the organization's data security plan. This level of access is for MANAGERS with authority over the business unit. The application refers to this access level as business unit.