I think a lot of people here haven't listened to the clip very carefully.
Nowhere in that clip does Ned say that the wood composition of the body (i.e. the type of wood) is not important. He doesn't address the neck at all.
What he is saying essentially, is that you do not need a full size body to make a good sounding bass. In other words, while the body of an acoustic guitar is an absolutely essential part of creating the tone, a bass can be made with a very small body without it affecting tone all that much.
Now I would still argue that there are probably tonal differences between a bass with a full-sized body and an identical bass where much of the body mass has been cut off, but I think in general that he is right in that you don't absolutely have to have a full sized body in an electric instrument, whereas you cannot say the same about an acoustic one.
A bunch of folks here are putting words in his mouth. He never said the material the bass was made out of wasn't important. Indeed, the whole idea for the original Steinberger basses was to use a different material -- everything else like the headless design and the bridge resulted from his desire to use composites.
+1

