Print designers coming to the web, often have problems with this. Using fonts that won't render clearly, justifying columns, tiny gray text on white, a background that stops repeating after 1600px (the size of their monitor). Fixed width designs wider than 1200pixels. Very uneconomic gradients.
For someone who calls herself/himself a web designer these problems should be non-existent. If you don't know the medium for which you design and its limitations, you are making a flyer in Photoshop, not a webdesign.
Beautiful functional web design follows from real content and interacting with the page like a user. A web designer who doesn't venture beyond Photoshop will likely produce very one-dimensional designs.
A front-end developer should know a lot about design. Not as a suggestion, but as a given. To do a design justice, you have to translate it with care. I see the need for overlap more for back-end developers and front-end developers. Back-end needs to understand valid HTML and front-end needs to work with a template engine and do data requests.
For web designers and front end engineers, a full overlap should be a given, and it isn't that rare to find one who can do both. Now back-end vs. web design is a chasm too wide to cross, realistically.