I consider a degree to be proof that a) you can be trained, b) you can start and complete a program of study (i.e., project), and c) you have a good idea of what you're talking about.
It doesn't mean you are any good at it (or even above average, really). It doesn't mean that you're a programmer or a scientist. It just means that you're trainable.
And in that regard, the major you choose doesn't really matter one bit. You can get a degree in biology or theater or business, and you'd still be trainable. You might not have the fundamentals, but those are easily taught. If you can learn bio-chemistry, then you can learn FSMs and pick up the fundamentals of programming.
So as others have pointed out, it's not a computer science degree that matters. It's trainability and the capacity and desire to learn that matter. I'd hire a hard-working, self-directed, knowledge-hungry theatre major over an entitled, I-don't-want-to-do-anything-but-program CS major any day of the week.