I have published three books with traditional literary presses. I have published one book with an academic press (Johns Hopkins). I am now taking matters into my own hands and have published my newest novel myself. It has been (substantively and copy) edited by three highly qualified editors from the book business, and the design and layout has been done professionally. The reviews (from intelligent readers who are not related to me ;) ) have been really good so far. As a self-published author I receive a significantly greater proportion of the proceeds than I would receive through a publisher, I can get the book out two years before a publisher would ever be able to get around to it, and I find I care more about promoting my book when I can monitor sales on a daily basis. The world is changing and while self-publishing and being traditionally published are not the same thing because there is no third party vetting the book BEFORE it is published, there are now thousands of people vetting it AFTER it is published, so the good books will still rise to the top. How they get there is immaterial. And as far as I can tell, most readers today have no idea if they are reading a self-published or established-press book.

TL;DR - "Self-published" is not the same as "other-published," but it doesn't matter any more.