Considering that the primary purpose of the Prime video app on the PS3 seems to be to make you think you can stream something, then tell you you have to buy it

Considering that the primary purpose of the Prime video app on the PS3 seems to be to make you think you can stream something, then tell you you have to buy it right before you start watching, I'd say this is likely correct. The "free" prime streaming seems to just be a marketing tool for getting you into their video-buying app. I'd be surprised if they have much interest in streaming anywhere where they can't push paid videos without having someone else take a cut.