I just went back to Apple and told them to google this thread, so they can see that it is not just an issue with a single individual, it is relatively widespread. And sudden on-set. May 31st it worked. June 1st there was a firmware update in the afternoon (it was also working fine in the morning!!) to the Apple TV, and that evening homesharing started the "authorization required" pop-up on any movies or TV shows. Now I can directly stream purchased movies just fine, but it eats my data and the resolution suffers (I'm on ADSL so I have to lower the resolution to 720p or it buffers constantly).
I haven't tried to homeshare to my iPad or my phone - I don't want to watch movies on my phone so that has never been in my list of things to try. And I can't home share on my iPad when I'm not home, and since if I'm home, I don't homeshare to my iPad, I watch my TV, that also has never been top of my list to try. But I will try them now, the iPad at least - the less I muck about with my iPhone settings, the happier I am.
I told them I am away for a week, but when I get back, I will check. If it still isn't working, I will be calling. I will become a thorn in their side every day. I can afford to waste a half hour in the morning.... I'm retired, so I have lots of time first thing in the morning. Case in point... I'm here again. So if you haven't contacted apple support about this, do it. If the wheel doesn't squeak, no one will oil it.