Cooper, can you clarify what you mean by "headers"? You seem to be jumping all over the place and it's confusing me. Let's go back to your example:
The alt text for the branding logo (and essentially the name of the site) is not marked up in any way even though it's at the top of the page. Using your methodology, turning off styles and images would result in site name and tagline being visually equivalent. That is what I was referring to when I said it didn't seem right to me. That isn't to say it should necessarily be a h1 (so please don't counter that) but it's surely semantically different to and more important than body text.
<img src="" alt="" width="" height="" /><!-- Branding logo -->
<p>......</p><!-- Tagline + hidden information --><!-- EDITED TO NOT CONFUSE ANYONE -->