Judging from a thread that's gone to about 160 posts on Amazon, (and my own experience), here is what happened.
First there was an update which broke Instant Video in Linux. They reacted to complaints with apologies and saying that it would be reported to their engineers. Then, they sent a follow up email, a month or two afterwards, saying it was fixed, which, apparently, it was. Then, they broke it again with another update.
At this point, they began responding to complaints with statements that Linux was not officially supported. Many people were able to (and are still able to) get it to work by installing some hal packages in Debian based distros and some fake hal packages in Fedora.
By this point, once they said they weren't officially supporting Linux, I gave up and will no longer buy or rent videos from them. At one point during this time, though, I was able to play videos through FreeBSD 9.x, where I had HAL running with X. Currently, everything I have at home is 10, not using HAL, and not working with it.
And so, content providers, in yet another effort to protect their content, drive another group of people away, some of whom, will no doubt, pirate what they would have been willing to legally buy.
I would, quite seriously, recommend that you write to Amazon and complain. They'll write back and tell you that it's not officially supported, but still, if enough people complain, who knows, especially now that they're raising (or have raised) Amazon Prime's price by $20-30. Maybe they can hire some Hulu engineers to figure out how they're able to give a cross platform experience.
Amazon thread here.
http://www.amazon.com/forum/amazon%20vi ... YET6CH0PQI
