This issue has two potential causes:
1) With version 6.2.0.1057 the import service does not support sites that use claims-based authentication and SP2013 sites all use claims-based by default. NMSP must be upgraded to 6.2.0.1060
2) The service account running the Import Service service application may not have access to the SharePoint content database.
This issue was resolved and fixed with version 6.2.0.1060. You must use this version or higher if you want to use the Import Service and SharePoint 2013.
In the event of a permission issue please review the SQL Server instance to ensure that the service account has dbowner permission to the SharePoint content database.
