Do all publishers charge writers to publish their work?
According to some, it is a legitimate part of doing business in today's world, and I've just had a rather heated debate with a publisher who feels that not charging is impossible. 
Hmmm! I have been known for my Polly Anna tendencies, but a work should be accepted because a publisher feels that their investment in editing, typesetting, design, printing and royalty costs will be returned by enough readers purchasing the title. We all make mistakes, and invest sometimes in a book that barely covers the first stage of these costs. As a result, we rely on bigger sales from other titles to offset these costs.
However, asking a writer to contribute to the printing costs veers too close to vanity publishing.
As a small publisher following a slightly different model from most - taking manuscripts only from new writers and asking book groups to decide what we should put to print - we are occasionally asked if we charge writers for print costs. 
No question makes me stand on my toes and yell more vehemently, "ABSOLUTELY NOT!"
Credibility in this business matters.