Long-term potentiality is not the point of disagreement. The disagreement is that individual memories are not recalled, as they are not stored, per se. The idea is that neurons acclimate to inputs, so that when we "recall" them we are not retrieving a "memory" from a storage location but instead are being activated in a way that allows us to preform a learned action.

I imagine those marble/cardboard diagrams of logic gates, where the cardboard flap will be left in a particular position after a marble has passed. In this way you can add numbers by dropping marbles into the appropriate input slots. Yet in this way, one could not derive prior calculations, as it does not store this information anywhere.