The Search Service crawls the object model, not the SQL server directly. Thus, the SQL authentication is occurring using the normal farm/app pool account.
The Search service account is used to connect to the search db, but it never actually connects to the content databases directly.
SharePoint Server search service account
The SharePoint Server 2010 Search service account is used as the service account for the SharePoint Server 2010 Search service. The SharePoint Server Search Service is an NT Service, which is used by all Search Service Applications. For any given server, there is only one instance of this service. The SharePoint Server 2010 search service account requires the following permission configuration setting: The SharePoint Server 2010 search service account is granted access to the propagation location share (or shares) on all search query servers in a farm.
The following machine-level permission is configured automatically: The SharePoint Server 2010 search service account is a member of WSS_WPG.
The following SQL Server and database permissions are configured automatically:
This account is assigned to the WSS_CONTENT_APPLICATION_POOLS role associated with the farm configuration database.
This account is assigned to the WSS_CONTENT_APPLICATION_POOLS role associated with the SharePoint_Admin content database.