The Emperor's New Wonder Show

I'm currently making my way through Cervantes's Interludes.  Overall, it's kind of meh.  However, one play in particular — The Wonder Show — has distinct parallels to Hans Christian Anderson's The Emperor's New Clothes.

Given that the plays were published in 1615 (though written earlier), and Anderson wasn't born until almost two centuries later, I can't help but wonder if there's some common source — a folk tale of some sort — that both were mining when they wrote their pieces.