Does acid and base react directly, or do they react first with water?
With strong bases and acids, only $\ce{OH-}$ and $\ce{H3O+}$ react, right, because $\ce{AH}$ and $\ce{B}$ (practically) don't exist in aqueous solution. 

For weak acids and bases, that's not true, but still there the water can "transport" protons much faster between AH and B than direct exchange after diffusion. As was noted below, that's called the Grotthuss mechanism.

So yes, you are right, but the formula (1) is a valid simplification which is, for most uses, as good.