Black holes have more states than those giving the Bekenstein-Hawking entropy: a simple argument

It is often assumed that the maximum number of independent states a black hole may contain is $N_{BH}=e^{S_{BH}}$, where $S_{BH}=A\mathrm{/}4$ is the Bekenstein-Hawking entropy and $A$ the horizon area in Planck units. I present a simple and straightforward argument showing that the number of states that can be distinguished by local observers inside the hole must be greater than this number.