Dan, pil pil is a method of cooking, not a recipe per se. It originally was Basque, then spread throughout Spain.
Essentially you cook seafood (shrimp and salt cod are the two most commonly done this way) in a comparatively large amount of olive oil, along with garlic and hot (red) chilis. The oil is constantly swirled, and the proteins extracted from the seafood (particularly when done with the cod) combine with the oil to form the sauce that foodiecutie referred to. To be absolutely accurate it should be made in a cazuala---sort of a clay skillet that's glazed all over except the bottom. When served as a tapa, small cazualas (like 3-4 inches) are used.
Eating shell-on shrimp made this way could be really messy, IMO.
Anyway, it's not really a matter of butter vs olive oil. If you want to make this dish, then you use olive oil, it's the only way to develop the unique sauce. If you want to use butter, than it's a different dish with a totally different flavor profile.
In Zane's case, he was following somebody else's adaptation of pil pil, and olive oil was the correct choice. There just wasn't enough of it (not his fault) to create the sizzling shrimp of Iberian fame and legend.