The debate about tone woods is basically a sort of religious war - the sort that arises between people who are perhaps overly passionate about a subject. Like Macs and PCs, VHS or Beta Max, GM or Ford, it's just one of those things that is going to divide people.
Seems to me the science leans towards the 'negligible difference' guys (and I suspect 'negligible' is a better answer than 'none'), but there is a very small amount of actual scientific, controlled, experimental evidence to prove the case either way. The Chapman video is an attempt to show what most people in the business of selling the difference between a $300 guitar and a $3000 guitar believe to be true, but on it's own it's not good enough. Guitars may have identical specs, but without testing more guitars to see the random difference from guitar to guitar based on differences that might arise in manufacturing, it means very little.
To do a test that could actually be scientifically accepted, you'd need to test the sound of a guitar where the only thing that changes is the wood. All other variables have to remain the same. Same nut, same bridge, same setup, same wiring, same glue, same screws. Two 'identical spec' guitars are not close enough - it needs to be the same guitar with nothing changed but wood.
A better test would be to simply screw a pickup to a block of wood and set up a single string (not need for a nut or bridge - a couple of knife edges would do. Record the sound wave accurately using a computer oscilloscope via a pickup, not a human ear through YouTube. Change the wood - but nothing else. Everything else needs to stay the same to the millimetre or less. Look at the magnetic 'sound' wave produced by the cable (no need to actually listen to sound, as that's just adding variables introduced by an amp).
Repeat with many versions of the test woods, not just one subject. Compare the variation in tone produced by 'guitars' with the same wood vs variation between woods, and see if the difference is statistically significant.
My guess would be that, properly tested, the difference would be negligible. My reasoning is that solid body electric guitar pickups, and indeed solid body guitars, were designed specifically with the intention of NOT resonating. Early guitars had massive feedback issues - so they cut out the resonant boards, and designed pickups that were meant to 'pick up' only the magnetic distortion created by a moving string, and nothing else. But that is only my hypothesis completely untested by valid experimental data. I doubt anybody has done a proper test, but I'd be interested to see one if they have.
As a control you might include a variety of 'strings' which are stung to some sort of non-resonant surface that is not wood at all, to prove you can actually reproduce multiple instances of identical sounds in identical circumstances when something is set up by human hand.
What we have instead are some very angry people (who, by the by, should maybe consider getting out and relaxing more) competing over whiteboard drawings to 'prove scientifically' one side or the other. Real scientists know that the proof is through experimental data, not whiteboard hypotheses, however well constructed.