You're right in that its based on perceptual hashing (likely due to a cursory reading of Apple's documentation). What you're clearly confused about is that you don't understand what perceptual hashing is. It doesn't "say the other to make people... more comfortable with the concept." They are explaining, in laymen's terms, the general idea behind the concept.
Here's a well-cited paper covering the topic:
https://ieeexplore.ieee.org/document/1709989
Here's a tl;dr: a perceptual hashing algorithm is one that provides an efficient means of finding matches of
exact images, even in the presence of alterations on
those images. They are not designed for generalizing to match similar images in the sense that they share certain visual characteristics, or even to images containing similar features. There
are classes of algorithms that do those things, but the
whole point of a perceptual
hash is that it can distinguish true matches from those that are
very close to originals.
Delusion is a funny thing; it's often we see others as deluded when we ourselves have misappropriated facts.