You didn't "parse HTML" with a regex; you created a solution to fix a very narrowly circumscribed problem by pattern matching on some string inputs. Big difference. Were an easy to use HTML parser (or likely lexer) readily available there'd be little excuse to cut corners as the proper solution would likely be far easier to prove correct (formally or informally) than the regex hack. (Full disclosure: I've written an HTML5-compliant streaming HTML lexer precisely so I--and others--would have less reason to depend on regex hacks in security scanners.)
The article says that the Linux approach proved good enough. No, it didn't. Linux has turned into a nightmare of security vulnerabilities, on par with Windows 95, just as originally prophesied. We only tell ourselves it's good enough because we're unwilling to admit we're where at. Remember when Linux and open source were paragons of security? Man, how times have changed....
But now we have a formally verified operating system in seL4, which is... [wait for it...] a microkernel. Of course, it's difficult to use as a general purpose OS, though not far from where Linux was in the 1990s. In time we'll get there. In the meantime no good comes from lying to ourselves about the nature of our solutions.