According to some of the web-sites, the only time you're considered published is when the author is published thru a "Traditional" publisher. If an author uses any other avenue, such as POD (publish on demand) companies, vanity or subsidy presses, the author(s) will NOT be recognized as a "published" author and the label "self-published" will be stamp on the author like a scarlet letter.

In addition these bloggers claim that no agent(s) will even consider looking at the book for representation.    

Facts:

These remarks are false and self serving. An author is published once he, she or they get their ISBN number and the book is released. Released in any media form. ie. hardcopy, audio, e-book, etc.  There are many author(s) who had their book "self-publish" and they're considered published. I would point out that the Bible is one example. Rick Warren's book is another. There are thousands of books that got their start using publishers that were not considered "Traditional".

Yes there are agents that will not represent these author(s) but the reason is more likely to be that the book isn't strong enough, good enough or it isn't what the agent is looking for.

Additionally, some simple research of some of these bloggers shows that they're are using "non-traditional" methods to publish their books. Such as e-books, e-zines and of course the pay to publish companies. Very few of them have "traditional" contracts.  Some of the bloggers openly advertise for these publishers and some companies in return advertise on those blog sites. This is known as having a private agenda.