The reason this phrase is so catchy is that it's counter-intuitive, and easily proven to be true. People love to use it as a "gotcha" phrase, PRECISELY because in regular life correlation does in fact usually imply causation.
I agree, and this cannot be overstated. I worry that the use of this phrase is almost more dangerous than the mistaken belief that correlation does imply causation.
To be precise, in most of the examples people love to trot out, correlation does imply causation, just not direct causation. A and B might be correlated because they are both caused by the same thing. While a correlation between obesity and TV watching doesn't imply that TV watching causes obesity, the correlation is good evidence that one causes the other or that there is a third thing, laziness perhaps, that causes both.
Of course there are counter examples to this assumption, called Reichenbach's principle, but they are even more rare.