I'm absolutely positive you don't need any amount of BP before engaging in the Special Battle. Otherwise, the rest of those requirements sound legit, though I seem to recall not filling several a few of them and still being able to fight in the Special Battle. I'm honestly flabbergasted right now. I've never heard of anyone having trouble with this.
I'll look into it, but from personal experience, I don't have any further advice at this time. I hope you figure it out.