Took me a while to parse but I think he means they taped paper to the floor, then observed that the paper was still on the floor (as opposed to the ceiling) after the elevator looped around. The entire elevator was carpeted so it wasn't obvious if this would be the case or if indeed the elevator flipped over before beginning its descent.

Not OP, but here's how I think it worked:

There are effectively two vertical shafts, and the elevator car goes up one and down the other. If the car flipped over as it goes over the top to the other shaft, then what was the floor would become the ceiling. So, tape something to the floor to identify it as it's going up, then wait for that car to come down the other shaft and look at where your identifying paper is.

It does seem pretty obvious that it wouldn't flip over - that seems like an insanely dangerous design.

No ... since the elevator compartments were completely carpet covered, we wanted to make sure they didn't flip over when then went around the top and bottom (and yes it was taped to the floor).