Not sure about the FTB specifically, but in my experience centrelink employees rarely know what they are talking about. I was told on the phone that the child care tax rebate couldn't be processed until after we had done our tax, about 5 days later it was in our account. We still hadn't done our tax???
Did you fill in forms earlier in the year? I think I was eligible for FTB B, but never filled in any forms as I figured it was easier not dealing with centrelink.