As a Bard myself, I'd say that she's only partially right. The amount of hate generated by songs is miniscule. We're talking, a single Provoke will out-hate every song in a Bard's ******* - even with Soul Voice running.
I typically sing anywhere from 8-10 songs per battle (some buffs, some debuffs) and the creature will never bat a lash at me. Figure in that, as /BRD, this person's songs were only half as effective and I doubt they make very good hate-management tools. I'd say your Mithra tank was just really good at managing hate with her other tools.