This is only anecdotal evidence but from my past encounters with programmers at various workplaces the programmers that understand the fundamentals of parsing and interpreting seem to be overall better programmers. They also tend to be less religious about their tools. My subjective experience indicates they tend to write better code as well. I've mostly worked with application programmers and I know this is a very limited sub-discipline of programming in general so take my limited experience for what it is and nothing more.
What are some other foundational components of CS that tend to be correlated with programming skill and ability? I'm assuming some basic understanding of basic data structures so that's a given.