The problem with statements like these is that the term 'CS' has become so wide as to be almost meaningless. It is perfectly possible to get a 'CS' degree by taking a lot of courses focusing on software design, software project management and UX and interaction design, all of which would be very useful as a web developer.

You can also get a 'CS' degree by taking a lot of math heavy theory course, or hardware and compiler courses, which would be much less useful when working as a web developer.

The advice I would give is that if you know you want to do web development and you want to get a CS degree, you're best served to keep your end goal in mind when choosing what courses (or even school) you decided to go for.