Not watched the video but sure, a coil will be sensitive to vibrating strings as soon as they're magnetized.
The proposition that magnet type has no real effect on the process is what is troubling. I can defiantly hear a difference between a ceramic and an A2 magnet.
This "proposition" is generally not true ["generally" meaning:
for coils directly paired with magnets. Regarding
separate coils, see my afterthought comment in post 10 below].
Ferrite / ceramic magnets won't increase the inductance of coils but are typically very strong. AlNi(Co) magnets (and other alloys including iron) are weaker and increase the inductance while contributing to Foucault currents (eddy currents). These measurable physical realities change the frequency of resonant peaks and their Q factor but also what guitarists perceive as "dynamics": an impulse response of pickup with ceramic mag then with AlNiCo won't be the same and the sound will be affacted accordingly.
There are ways to mimic the effects of AlNi(Co) with ceramic magnets + added components,
to some extent. But the difference can't be denied [unless one dissociates coils from magnets].
As a Zexcoil link has been provided above, below is another one, showing changes in the factors evoked above according to the types of magnets used. Graphs show clear differences and they translate what can objectively be heard, since the resonant peak of a pickup defines a lot of its tonal personality (DiMarzio was already stating that more than 40 years ago).
Zexcoil Guitar Pickups - Dr. Lawing's Blog Posts
lawingmusicalproducts.com
Subjective perception is something else: we hear things differently (with variable audiograms susceptible to cause cases of tone deafness for sensorial reasons) and a soft playing with largely neuter some differences, for instance.
EDIT- Just saw the video was from Waylon Mc Pherson. I must say that I appreciate his work and videos, globally. His contributions are a goldmine. My reaction above is only about the idea discussed here in this topic...