The level of access to your people database is determined by which security model you are using. By default, your nation uses the functional security model. You can switch to the data security model from People > More > Point people. At the bottom of the page, below the list of point people in your nation, you'll have the option to switch between models.
Using the functional security model, anyone who has access to the control panel has access to the full supporter database. The intern/leader/staffer permission levels restrict who can publish information, and who can view financial data. There is no segmenting of the database in a nation to only allow access to certain people within those permission levels.
If you use the data security model, you can segment access to your database. Learn more about the different permission levels available in each model.