"Only Accepting Published Authors"

Technically they don't say that... they say published authors. So if you have a worthwhile publication credit then go for it. I suspect they are basically looking to cut thier pile of manuscripts down to ones that may be worth reading so ask for the kudos of a previous credit or an agent to narrow the field.

I say go for it...

And you could also send to some agents as well which would also get you past this sort of block.

I imagine a magazine credit works.

Just start your query / cover letter with. "I have been published in____" (for magzines0 or "I am the author of ______" if it's a novel. Give the publisher's name and let the acquisitions dept of the press you're querying determine if it works as a publishing credit or not.