Do you have to have a degree to land a job at a publishing house?

I'm a fulltime Online (web) writer and freelance Journo (magazines). However, I'd love to land a fulltime job at a publishing house as a writer. I've been published by a number of well-established magazines and I'm working on a feature article for a well-known newspaper at the moment. I've tried submitting my CV for jobs at various publishing houses but I never seem to land an interview - most ask for a degree - I have a diploma and some other certificates. Surely, passion and talent should count? What am I doing wrong?