It's been several years since I've had tape, but it sounds to me like the DBA has done everything correctly for 6 channels. The problem, if you can call it a problem, is that the backup server (media server) has only or is allowed only 3 tape drives for the restore. On the other hand, perhaps the files being requested on the 6 channels are stored on only 3 tapes. You can ask for 6 at a time, but each tape can only be in one place at any point in time.
There's nothing special about RMAN ... it's just a program that backs up the various parts of a database, keeps track of the backups, and when it comes time to recover a database, or a portion of it, requests the images from the backup system.
IMHO, the DBA was totally wrong to be screaming, but is probably right that this is a NetBackup issue (if he thinks the performance of 6 active streams will significantly outperform 3 active streams -- it might).
Guaranteeing that 6 backups streams will be written to 6 separate tapes could be a daunting task. I avoided this for restores of recently backups, when I had tape, by having backups go to a disk pool and then later to go tape.