I never said it was the best way, but using an <img> element with appropriate alt text was and is a valid way to replace text with a graphic for supporting user-agents.
If you want to put that text in H1 tags that’s fine although that text is usually a link so once again, not an H1 situation because it’s not a heading.
Huh? Text-replaced-by-images generally occurs in one of two places - it could be for action buttons (which, as you say, would be links) - or it could be used for headings, à la CSS Zen Garden, which would not by and large be links. And so replacing the text with an image inside an <h1> element would be entirely appropriate. And while, as I said, the better techniques use CSS to achieve that, there is nothing intrinsically wrong with using an <img> element. Can you enlighten us as to why you are so outraged by that?
Please correct me though if there was a pre-CSS image replacement technique that I’m not aware of.
Um … the <img> element 
No, it wouldn’t. H1 is a text formatting tag and an alt desc is not text in a presentational sense.
<h1> is not a text formatting tag. I know this, because it is allowed and recommended in HTML 4.01 Strict, which formatting tags are not. Formatting tags are generally deprecated, or deprecated in certain uses, such as <font>, <b>, <center> and so on. What <h1> is is a semantic markup tag, which gives the meaning of its contents. It does not specify any formatting.
And does “an alt desc is not text in a presentational sense” actually make sense? Because I can’t see any there. The alt text is text, it is the text to be used if the image is unavailable, and so should be considered as equivalent to the image in both content and context. If you were using the text that is in the alt just as text, and forgoing the image replacement, and you would put it in an <h1>, then it is absolutely right that you can put the <img> element in the <h1>.
What is it that you do for a living?
That’s none of your business, particularly when written so clearly intending to cause offence, but it is nothing to do with web design.