How does only one mesh with the FAQ? I'm not sure what your point is there, since as far as I know it wasn't dealt with directly in the FAQ. It was however covered quite thoroughly in the rules.
It is entirely possible to deal one damage card at a time, resolving each before drawing the next one, and still end up with damage exceeding the hull value. It can occur either because of a Direct Hit critical result, or as the result of Simultaneous Fire situations.
The argument for continuing to draw damage cards rests entirely on the wording "or greater than". The following paragraph includes that phrase, but is actually pretty unambiguous about when ships are removed. They go away the moment they have sufficient damage.
When the number of Damage cards dealt to a ship is equal to or greater than its hull value, the ship is immediately destroyed (faceup and facedown cards count toward this total). Immediately remove the destroyed ship from the play area, discard all of its Damage cards to a faceup discard pile next to the Damage deck, and return all of its tokens to their respective supplies.
Also, both in section 7 and in the following section it is clear that each card is resolved one at a time. It even goes so far as to bold the print stating as much.
When a ship suffers damage or critical damage, it suffers them one at a time following these steps. The ship must suffer all normal damage before suffering any critical damage.