I wasn't sure if this is the correct behavior.

If I choose red as Matching Braces Background color in the HTML editor and I click in the <div class="cornerHeader BRHeader"> shown below what should be highlighing?

    <div class="cornerHeader BRHeader"></div>

here is what I see for the highlighting

    <div class="cornerHeader BRHeader"></div>

When I use the html editor it highlights, but it skips any class or style within the div, and picks up the > and the </div>

see attached.

(The version of Dreamweaver I use doesn't highlight matching braces. I don't use other IDEs)