I don't think they want to compete with anyone, and weren't trying to goad WalMart into doing anything. The response from Amazon was just a way to spin WalMart's promotion into another proof that Amazon (and shopping online) is superior.
I agree in regards to goading but it's kinda obvious that Amazon is trying to sign up as many customers for Prime before the competition (Walmart, Jet, and others) can lay their hands on them.
They prefer not to have to compete.
Obviously nobody enjoys competing, but when a company is eating up your market share, all you wanna do is compete.