I've been told that Windows Server 2008 and newer uses the BITS service to transfer files that are backed up to a UNC share (using Windows server backup/NTbackup) but I can't find any documentation to support this. Is this true? If so, is it the default or does it require additional configuration of the backup job to use the service?
The information you were provided is inaccurate. Background Intelligent Transfer Service (BITS) is not used by Windows Server Backup in any way.
Windows Server Backup was introduced in Windows Server 2008 (and Windows Vista) as a replacement for the old "NTBackup" utility and the derived versions present in Windows 2000 Server and Windows Server 2003. It was significantly revised in Windows Server 2008 R2 and continues to be present in current versions of Windows Server.
It's difficult to "prove a negative" here, in terms of giving you a link to a Microsoft document that says "Windows Server Backup doesn't use BITS" because no such document exists. Windows Server Backup creates virtual hard drive (VHD) files and loads them with the contents of the filesystem being backed-up. On locally-mounted volumes serving as the backup destination multiple generations of backup are able to be stored in one location (by virtue of the Volume Shadow Copy Services (VSS) functionality). Remotely-mounted volumes (over SMB) serving as the backup destination do not have this capability and can only store a single generation of backup per location.