I think we are battling terminology here. Most quadrature encoders I have seen determine direction by which of the two square waves gets a rising (or falling) edge first. In firmware, I have done this by XOR'ing with the previous state. The frequency of the square wave determines the rotation rate.
I haven't seen one that uses two different polarity (wrt ground) squarewaves, but there's a lot of stuff I haven't seen out there.
