According to http://confluence.atlassian.com/display/CONF20/Site+Administrators+and+their+permissions, there is no way to limit these users from access to all spaces and pages:

"Site administrators have complete access to Confluence regardless of any site or space level restrictive permissions."

We would like to add sensitive data, including board reports and financial data, to a space limited to a handful of people, and these people only, site administrator or not.

Please! This is the only way we can move all our data into our Confluence installation and not have to keep some data elsewhere.