Traditionally, we'll apply typographic styles to elements like strong, em, p, ul, h1, h2, h3 etc, in the global scope. We are adding these styles to the elements globally. We think to ourselves "we're using the cascade!" and wrongly thinking that we're saving lines of code in the long run.
So the argument is to only style individual blocks of text, instead of saying "All H1 elements everywhere on this page will have this style". His "copy" class removes all typographical styling, so whatever styles you apply to a block will work without having to remove e.g. bullets from a list manually every time. (edited)
Regardless, the tone of the post reminds me of something I've done on a few occasions: writing entirely domain-specific XML, then styling it throughout with CSS into something presentable. It's a bit of a pain, and I'm sure it'd fail completely in older browsers, but it completely avoids the slightly-unpredictable nature of default styles.