Perturbations do exist and they add up in the PID feedback loop. For example you can see in the video that the way each box is handled varies and that the robot reorients itself to pick/drop boxes.
Consider a simpler 1 dimensional example: https://youtu.be/JpNAhKT7yY4?t=101 (warning, loud). You can observe the system adjusting to the hits by the person, but also when left alone it will have to adjust to accumulating externalities like gravity. Also note the natural/biological looking swaying motion that results.
You know, sometimes you see a solution, and it's just so elegant... This isn't elegant, or brilliant. This is an attempt to solve self-imposed, artificial problems.
P.S. people who liked your pendulum video (I did), might also enjoy this drone pole acrobatics video: