Most 'Web Designers' that are actually 'Web Developers' can't design for toffee - yep. It's ridiculous to say most 'Web Designers' are pretty crap designers, it's just ignorant and silly.
Most places will function with a Designer that is a designer foremost perhaps with some basic HTML/CSS skills and then a Developer to do the rest.
You need to have a good knowledge of design to be able to design a website well, having the ability to code and create a website doesn't mean you are a good web 'designer'.
A solid foundation in design is needed, and I bet most 'Web Designers' out there that are any good have 'Graphic Design Degrees/Principles/Basis/Training/Self-Taught/Whatever.'