Notice that in the question they did not use the word "Conjugate" in any of the answers. This is really important.
HSO4 is indeed the "conjugate base" of H2SO4. However, removing its relevancy from H2SO4, and observing HSO4 on its own, it must be considered an acid, (a weak acid at that) since it has a H to donate which will partially dissociate in an aqueous solution, just as the answer describes. That's the property of an acid, not a base.
Hope this helps clear it up.