I think you could never assume very much if somebody just said they were published, but not what IN.  What if it was the school paper or a newspaper needed a photo of Alcatraz to illustrate something and you happened to have a decent photo up and they asked if they could use it (I've had this happen to me repeatedly).  Is that impressive or not? 

What if you've had six photos published in a whitewater magazine because you wrote an article about some stupid dangerous trip you made and included six photos.  Does that make you a published photographer?  What if the pictures sucked but the story was compelling enough they didn't really care?  What if the readership of the magazine's very small - smaller than many online sites?

Anyway, without context there's really no telling if it means anything.  Just look at their work and decide for yourself if it's any good or not.

JD wrote:

In todays or even yesterdays market the term "published" means different things to different folks.

I've had images images in the newspaper, used to be a contract photographer for a paper in PA and I've had product images in catalogs, but as far as I'm concerned, I've not yet been published.

My thoughts exactly.  I have done a lot of online content for a website.  Also I did an ad for that same company that was printed in a magazine.  I don't think that I am "published".  I was just confused about it because I have seen so many other photographers say the were published and its a small blurb or article on some website.  And the only thread on "that other site" that had any information was two years old.   I think I will pose this question there and see what kind of responses I will get.

I've worked for/with a lot of publications, the first in 1966. Newspapers, books and magazines are typically what people mean by "published." And even then, you need to be more specific when offering credentials to other publications.

The reason that "published" matters really isn't so much a matter of photographic ability, but rather the ability of a given photographer to provide images on time, in usable condition, for a given purpose. Having done work for a wire service or a newspaper or magazine or book publisher would mean considerably different things, even though some of the skills involved overlap.

Among those who are the recipients of résumés, nearly everybody claims to be "published." Most, as Roger said, are scoffed at and ignored. They'd be better off to say nothing about publication and to offer work samples.

Similarly, there's a wide gap in art shows. Something at the local coffee house might actually earn the photographer more money than one at a major museum. But the museum will appear on the résumé every time, while the coffee shop show may not.

What I prefer to use is "credits." You're far better off to list highlights of specific examples to show what you've accomplished.