I'm an Amazon Prime member, and have the Amazon app installed on my PS3, and linked my PS3 to my Amazon account. When I search a TV show/movie that's free streaming for Amazon Prime, it tells me I can buy the episodes on my PS3 and that it's free for Prime, but will not let me play anything via Prime.
An example is the Chappelle Show season 1. It says it's $1.99 an episode or free for Prime. When I click on it, it says it's $1.99 for the episode, and that it's free for Prime but won't let me click on Prime or click Play anywhere, my only option is to click Buy it Now.