Experience and the pretty obvious mechanics of it:
Pickups pick up what happens on the string.
What happens on the string is determined by the materials, geometry and construction of the guitar. Its a resonant feedback loop: the string is a very broadband oscillator, the guitar is not. The string forces the guitar to resonate, but it can do so with a very limited spectrum and dynamic envelope compared to the string, so when the guitar resonates and forces the string to do so (the resonant feedback part), it forces the string to take on only vibrational modes and dynamic envelopes that the guitar can support.
Subjectively, I've heard many pickups in many guitars, and any given pickup in my possession has been in at least 2 guitars (probably more), and any guitar in my possession will have had much more than two pickup. Both play a part, both have signature characteristics, guitar and pickup. You start to learn what the pickup will take with it wherever it goes when you've had it in a few guitars, and you hear how the guitar sounds and behaves no matter what pickup is in it. With each combination, I've never heard the exact same sound twice. Every one is unique. The differences can be small, but there are always differences.
More experience, and comment on his video:
Observation 1: disappointingly incoherent and rambling. Not a good sign.
2: the first thing that even resembles an empirical argument: stienberger has saddles with more mass. Just before he said the mass/density of the wood doesnt have an effect. Its extremely well established (in physics, which I suspect he has little to no knowledge of) that a harmonic oscillators mass affects its resonance. A: Make up your mind. B: No, hes wrong.
3: The nut has little, even arguably nothing to do with the behaviour of a fretted note.
4: Sustain is hardly the sole measure of a guitars sonic behaviour. There are LOTS of other variables.
5. The wall is not in the vibration path of the strings. Its not part of the resonant feedback loop with the string. It will be, no doubt, sapping some sustain as it simply has to be sapping some energy out, but he doesnt bother to actually measure anything, let alone in a variable controlled way. This depresses me. I wanted a better fight.
6. Fortunately, cotton and blubber dont resonate readily or transmit vibration well. Qualitatively, low quality and area contact with them cant be expected to have a significant damping influence on the structurally transmitted vibration of the guitars resonance, and so doesnt affect the resonant feedback between the guitar and strings. Put the blubber on the strings, or completely encase the guitar in it
ewwww
Anyway, does this guy have anything else to say...
7. 6000 square foot house is irrelevant. The contact area as a proportion of the guitars surface is relevant.
So,
No. Nothing more to say.
Hes not wrong that the nut and bridge have a significant impact, but this is just a hick that doesnt understand what hes talking about.
I would love to have seen someone do something with some substance and sense to it. Take a few guitars and a few pickups and swap them around with dynamic and spectral analysis of a DI from the guitar. Its easily done. I could do it with all my guitars in a few hours. You would have to control picking strength and choose a wide variety of frequency distributions and modal superpositions (the physics kind, not the musical kind), and you would then, with constant gain on the DI, analyse the decay of the waveform of each sample and the frequency response. With large enough dataset for each guitar-pickup combination, if you saw no measurable difference in the fourier transforms of the DIs, and no difference in dynamic envelope (initial volume and note decay behaviour) then you would have a case.
You would still be able to argue against that case, subject to the resolution of the analysis: human ears are really very good at this stuff already, but you would at least have a starting point.
This in conjunction with a double-blind test and you might actually have a decent case. Or rather, a decent test.
But no. A hick that doesnt understand harmonic oscillators, resonance, vibration transmission or guitars.
In the mean time, until someone can make a case for or against this with some actual $%&#ing evidence, I have ears, and my ears told me the first stuff I said, and still believe.