Conservation of archival material is a specialized field of work. We need to understand the structure and chemistry of paper, ink, binders, adhesives etc. This video is actually making a tough job seem quite easy.
Whenever we need to separate two surfaces/layers, we need to understand many things about those two surfaces. One of the very basic and most important is that according to the laws of physics, the thinner and weaker layer or surface would be sacrificed first whenever there are chances of damage.
In the case shown in the following video, the original letter is on a thinner paper as compared to the backing.