Dick Cheney basically pulled off a coup that day. George W Bush wasn't incapacitated. He never put Cheney in charge. But Cheney just took over. He started giving orders and everyone else was too stunned to do anything but follow.
No, this was an emergency that everyone was unprepared for, so they winged it. And they did alright, even though it was utter chaos. If the President has been at the WH, or in good enough communication with the WH, I'm pretty sure the VP would not have been anything like "in command", though the President might have delegated some authority to him. As it was, POTUS had to get to AF1 first, then in the air, and probably a lot of work had to be done to get connectivity back to the WH makeshift situation room.
You have to go back to Reagan getting shot for something just slightly closer to a coup attempt, when the Secretary State ran around saying he was in charge (but no one gave him the time of day). That must have looked rather strange to a lot of people, but since no one took him seriously, and since it wasn't that long after the JFK assassination, which meant everyone remembered the basic chain of succession, the fact that no one took Alexander seriously was exactly as it should have been. Alexander, however, really had no clue, and showed he was not capable in a crisis.