OK, let's assume that Arnie saw a gunman on the 6th floor. Since he asked Babs if she wanted to see a Secret Service agent, that's a reasonable assumption.
Now, he could have been wrong, just like he was mistaken about the age of the person on the other end of the floor. Or about how far the guman was from the window.
But let's say he was right.
What precludes the gunman from seeing BRW before BRW sees him? After all, Arnie only saw the gunman for a few seconds.
BRW is busy munching on his sammich and looking out the window, right ?
Maybe the gunman retreats into the stairwell contemplating what to do next and then luckily for him, BRW departs to join his buddies - and the plan is back on.
Possible ?