I hate to take sides in this, but by your own words, it's not good enough. Two different basses. That's not proof. Also, it's a Youtube clip with terrible audio quality.
If I had the capital right now, I'd go out and have four basses made for me, all of the exact same physical dimensions, hardware, and electronics setup (even down to using wire from the same spool), just with different wood used for the bodies. Neck and fingerboard wood would be constant. I would record one sound clip into Pro Tools from each, playing the exact same line, with my hand at the same position, with the same pickup blend and volume setting, and use that as an example. Then I would record ten different sound clips each, post them unlabeled on TB in a random order, and ask people to identify which body woods made which tone. The numbers would give us a rough idea of how distinct a difference wood makes on tone.
That, I believe, would be the kind of solid evidence that could possibly convince some of the skeptics, as long as every detail and step of the process is documented. I would then sell all those basses since I'm not made of money, then make four more nearly-identical instruments with different neck woods, and repeat the process. Then, lastly, repeat the experiment with different fretboard woods.
If only I had that kind of cash...