Yes, I am familiar with that rule and it makes sense. A curb bit is not appropriate for side to side contact, only straight back. It is a leverage bit and does not have any flexibility. When you pull on just one side, you torque the whole bit in the horse's mouth.
You need a more thorough understanding of how bits are meant to function. I suggest reading this thread. It is geared a little bit more for english riders, but most of this material translates to western riding as well. Bit Information (Snaffle and English-Type Bits)