First, it is just a quip and is incorrect. Google has a lot of very talented statisticians, information retrieval experts, linguists, economists, some psychologists, and others. These folks spend a lot of time educating a lot of non-statisticians about the difference between correlation and causation. Given that it's a large organization, there may be pockets, even big pockets, of ignorance, but the assertion is definitely false. Moreover, a lot of that education faces customers, especially advertisers.
The difference is extremely important. Just look at search results ranking, and allow me to extend beyond just "correlation" to include measures of similarity, scoring functions, etc. Some pages are measured to be good results for certain queries. These have a variety of predictor features that are important to their ranking. In contrast to these good pages that are good results for queries is a set of webpages that are pages that are very bad results for the same queries. However, creators of those pages spend a lot of effort to make them look like good pages from a numerical point of view, such as text matches, internet linkage, and more. However, just because these pages are numerically "similar" to good pages doesn't mean that these are, in fact, good pages. Therefore, Google has invested and will continue to invest a lot of effort determining what reasonable features distinguish (separate) good and bad pages.
This isn't quite correlation and causation, but it's deeper than that. Good pages for certain queries may map into a numerical space where they appear similar and distinct from many irrelevant or bad pages, but just because results are in the same region of the feature space does not imply they come from the same "high quality" subset of the web.
A very simple perspective is to address the ranking of the results. The best result should be first, but just because something is ranked first doesn't mean that it's the best result. By some metrics of scoring, you may find that Google's ranking is correlated to a golden standard of quality assessments, but that doesn't mean that their ranking implies that the results are truly in this order in terms of quality and relevance.
Update (third answer):
Over time, there is another aspect that affects all of us: it is that the top Google result may be deemed authoritative, because it is the top result on Google. Although link analysis (e.g. "PageRank" - one method for link analysis) is an attempt to reflect perceived authoritativeness, over time new pages on a topic may simply reinforce that link structure by linking to the top result on Google. A newer page that is more authoritative has a problem with the headstart relative to the first result. As Google wants to deliver the most relevant page at present, a variety of factors, including a so-called "rich-get-richer" phenomenon, arise due to an implicit effect of correlation on perceived causation.
Update (fourth answer):
I realized (for a comment below) that it might be useful to read Plato's Allegory of the Cave to get a sense of how to interpret correlation and causation as a result of "reflections/projections" of reality & how we (or our machines) perceive it. Correlation, strictly limited to Pearson's Correlation, is far too limited as an interpretation of the issue of misunderstanding association (broader than just correlation) and causation.