Generally good advice, but can be OK in specific situations where you have a known HTML structure and are just scraping some values out of it. This is not so much parsing HTML as it is matching the patterns of the values you want to extract.

A regex can be used effectively to tokenize XML-like markup, including a lot of HTML—sometimes called shallow parsing. https://stackoverflow.com/a/6638578/234823

Attribute value minimization would be one limitation, since that regex is for XML, but it's a more robust approach than writing naive "<x>.*</x>"-style regexes.