How many 'web designers' are actually print designers who have converted to web, and haven't grown with the web?
I think this should be a non-issue these days. If a designer has been working consistently for the past 15 years, I suspect they would have transitioned from print designer to a web designer. Either that, or if they are newer to the field, wouldn't they have learned web design.
UX is a completely different animal, though I see many designers who like to get involved and understand UX because it has a huge effect on what and how they design.