I'm not sure what stats you're looking at, but of the top 20 pitchers in K/9 last year, Lincecum, Verlander, Lester, Vazqeuz, Kershaw, Greinke, Nolasco, De La Rosa, Sherzer, Beckett, Johnson and Billingsley had a better FIP than they did an ERA. And of the top 10 pitchers in K/9 last year, 9 of them had a better FIP than ERA.
I wouldn't call that correlation zero.