Since the bridge and sometimes the pickups are mounted to the wood guitar body, the wood does affect the tone.
It becomes one of those discussions (dare I say, “arguments”) that are common in hi-fi circles regarding some of those really expensive snake oil hi-fi products. I’ve been part of THAT discussion since the early 70’s.
BTW, the youtube video with the blind A/B test is part four of a series here: https://www.youtube.com/watch?v=5vgwaiScrwA
It’s baseline guitar has a clear lexan body.
I don’t care what most people can detect when hearing a guitar playing. I only care what I hear and feel when I’m playing one. As far as trying to make audio judgments from videos, I gave up on that a long time ago and only trust my ears in live situations.