That is why the matrix is conveniently broken into specific sections.
Yes, it most certainly does. In the long run, the developer with the better grasp of fundamentals (e.g., discrete maths, data structures, algorithms and so on) will produce better code. NB, I'm not saying that the "naive" web coder can't produce good code. Nor am I implying that CS education always makes you a better developer. On average, however, that's exactly the case.
Even with generic web 2.0 stuff.
1) Do you receive magic fairy dust during college that makes you more productive and removes bugs from your code? No, I don't think so.
2) Will someone who knows the things taught in a typical 4-year undergraduate CS education be a better web developer? Obviously (?) yes; you can look at any of them and clearly see that they are good things to know. Will you point to some particular thing that you think is useless? Let me list some that seem reasonable for a lot of web development: non-trivial data structures, for understanding databases; experience with multiple languages; continuation-passing style; general system and network architecture (e.g. the OSI model) -- and so on.
If by "web developer" you mean writing http://www.hasthelhcdestroyedtheearth.com/ then I guess no, you don't need to know much about anything for that.