Data partitioning is not normally required to block end users seeing each others incidents. The search box in Web Desk can search them by number but the search box in Self Service (the only interface end users can access) will ONLY search your knowledge base.
Partitioning is normally based on groups so you are absolutely correct that switching to that group gives you access. A common scenario for analyst partitioning is that your analysts are only in the groups they require.
Another option you might want to look at is attribute privileges. You can enable any attribute on any object to be "privilege-able" via its properties in Object Designer and you can then limit which roles/groups can see and update the value. This is particularly useful for sensitive data on attributes on common objects.
I hope that helps.
That is a great description on the use of data partitioning. Thanks. Looks like I need to look at a new path for my project.