The assumption - which does not stand up to investigation - is that if you pay attention to one thing, you must be falling down on another. For instance, if you think about the people who use your site, you must be a bad designer. Or if you torture-test the backend, you probably don't even bother proofreading the text.
[I]t gets harder to build an effective team if the UI designer distrusts the graphic designer, who hates the writer, who can't stand the lead developer, who looks down his nose at the systems administrator, who's convinced that the information architect is a useless hack - and don't even ask what they all think of the client.
Basically, questioning why people think you won't do everything well if you do one particular thing well. To put it another way: you can have a beautiful design; standards-compliant and accessible markup; a robust back-end; useful content; and a rewarding user experience... all on the one project. You might even be able to have a happy client as well, although you might want to just shoot for the stuff that you can control.