It took me years to notice, but did you catch that the answer actually subtly misinterprets what the question is asking for?
Guy (in my reading) appears to talk about matching an entire HTML document with regex. Indeed, that is not possible due to the grammars involved. But that is not what was being asked.
What was being asked is whether the individual HTML tags can be parsed via regex. And to my understanding those are very much workable, and there's no grammar capability mismatch either.
I think even for single opening tags like asked there are impossible edge cases.
For example, this is perfectly valid XHTML:
<a href="/" title="<a /> />"></a>
The thing is, even when parsing html "correctly" (whatever that is) regexes will still be used. Sure, There will be a bunch of additional structures and mechanisms involved, but you will be identifying tokens via a bunch of regexes.
So yes, while it is an inspired comidic genius of a rant, and sort of informative in that it opens your eyes to the limitations of regexes, it sort of brushes under the rug all the places that those poor maligned regular expressions will be used when parsing html.