This article offers information regarding permissions related to Data Warehouse and Data Explorer. Permissions cannot be applied to data in Data Explorer, this is a case use for Ad Hoc reports.
If a user needs to run integrations but not see any data, only two permissions are required. Grant "Can run integrations, rules & jobs" under Data Warehouse permissions and "Data Warehouse" under Feature Access. As permissions cannot be applied to Data Explorer, be sure this is only given to users that should have unlimited access to data.
The access given under Data Access is in relation to Report Templates, Ad Hoc Reporting, and Input Templates.