It was actually invented by Coke for an ad campaign back in the 1930s - read about the history here.
Coke have never really sought to make the connection clear - the colours are arguably enough and the story works well as a low key meme. I remember talking about it to Stephen Jones when he was Cokes' UK marketing director and we felt it was hard to build the links without it sounding a little negative - so it stayed at a virtually subliminal level.
Enjoy a cold one today
UPDATE - Russell from the excellent Mobhappy points to a dissenting voice - maybe Coke just took something from popular culture and made it their own? Isn't that what traditional agencies do all the time?