Something that was mentioned but perhaps not clearly articulated in the acoustic guitar video, and that would apply equally to pianos, is the tailoring that can be done with hand built instruments. The two guitars in the video seemed to be very carefully built by somebody who seems to know what they are doing. I suspect that if you put 'barn' wood through a mass production process to build a guitar and then similarly built a guitar using high quality spruce, your chances of getting a better sounding instrument are higher with better materials. That said, you can always get lucky. I used to own a rather nice sounding, but cheap mass-produced (solid) mahogany top guitar. It did not have the complexity of my rather more expensive, carefully (but still factory) built (solid) spruce top guitar, but I did have a pang of regret when I sold it compared to having completely erased from my mind the spruce top Seagull (that I also sold). (Happily I still have, and love, my cedar top Seagull).
How does this compare to pianos? Well, how many times do you read that you should always buy the piano you have played, not the 'duplicate' they have in stock? And then, other factors can come into play when you get it home - humidity, furnishings, floor covering, tuning pitch, and so on. However, in my experience, a piano out of a 'low production volume' builder (of good reputation) is more likely to more easily have a more satisfactory sound than a mass produced model.