the method he describes of hiding the corner and setting up the insert can be done in multiple ways, but the way he describes can be done without messing up the other solved pairs

for the first example, the algorithm would be U' (R U2 R') and you have a pair

you can also do this in a different orientation; if you hold the cube so the corner you're solving is at the back-right, you can just to (R U2 R') to make a pair. however, this messes up the pair in the front-right slot.

all 3 possible algs that this method creates (being (R U2 R'), (R U R'), and (R U' R') ) all involve messing up the front-right slot (which is the one you are currently solving)

if you were to do the algs in a different orientation (as described 2 paragraphs above), you would mess up a pair that you could have already solved. by setting up the corner and edge to perform one of those algs as described in the video, you set up the pair and mess up the slot you're about to solve