The small pins are supposed to rest on the <i>ramp</i> of the heel receiver, not the horizontal surface at the bottom. I don't see how they could exert any lateral force. The small pins are supposed to be the primary downward load-bearers. The large spring-loaded pins are only supposed to hold your boot down in the binding.
When your tab broke, it allowed the boot to sit cockeyed in the binding, so all bets are off then.
As Fin says, the micro-sizing should do away with the side-to-side play. I haven't tried that yet.