As an Alabama fan, I laugh at this story.
People bitch and moan about Bama's "MNCs", but the 15 that are claimed were all recognized by a legitimate standard. Yes, many of the older ones were during seasons that had multiple (and in some cases more deserving) champions, or during years that Bama lost their bowl game. What haters are too ignorant to recognize is that those were the rules of the day, and you cannot retroactively take them away using today's criteria.
That being said, on what grounds could Auburn even remotely make a claim to 2004? The fact that they went undefeated? Yeah, ok, then add two more to Bama's total (1945, 1966) using that logic.
I don't know the history behind the older Auburn national championships, but if a legitimate agency using a legitimate standard of the day crowned them national champs in those years, then yes, they have grounds to claim them. 2004 is not one of those years.