Clarification of Pillbug movement rule in Hive
The piece that is moved by the Pillbug's special ability travels on top of the hive in the same way that a Beetle would. If there are Beetles at that level, you will have to move around them as you would during normal movement at ground level.

To illustrate this, I'll use the picture from the rules that you quoted:



In this example the Ant can be moved by the Pillbug ability. Now imagine two beetles (B) present on top of the white Bee and white Spider:



This would make the gap between those two stacks too small for the ant to pass through, thus violating the freedom of movement restriction.