If only it were that simple. If you google around non Apple forums, you'll find endless people with differing hardware with the same issues, or slight variations. avsforum is a good site as one of the HDMI gururs is there, check out the HDMI forum there as ask him questions. Here's a sample for you to read:
http://www.avsforum.com/avs-vb/archive/index.php/t-1286409.html
In here, you'll note how common the issue is (just one of hundreds of thousands of posts). Many problems are the EDID info, which the Gefen mentioned previously would likely solve. I know it SEEMS like change one variable, the system breaks, therefore it MUST be the one variable, but, not the case with HDMI. You can find people with the same TV and Mac on the same os that works, you can find ones that do not work, etc. The problem MAY be Apple, it may also not be, perhaps the TV has a slightly out of spec HDMI implementation and while it may work with other hardware, in reality, it's not supposed to, etc. Adding intermediate HDMI devices such as AVRs, repeaters, etc only compllicate it more. And then you have HDCP issues on top of that. Plus, possible cable issues, length issues, etc.
We all wish HDMI were that simple (and really, it SHOULD be). Sounds so promising - one cable, how ideal. The reality is not so simple. And it's not limited to the Mini, to a specific TV, to Apple, to a certain video card, to a certain driver, etc. At times, on any platform or combincation of devices, an intermediate defvice is needed to just make it work as it should have in the first place. Sometimes, even though the only difference is the Mini, the problem actually lies elsewhere.
For the Yamaha RX-V467 - I see a number of messages on avsforum with differing HTPC issues and even green flickering (and one with blue). One guy says he got the Yamaha replaced and it solved his problem. Again, it does not matter if it works with another PC, that is the nature of how this all works.
Best suggestions is to ask on avsforum, in the HDMI forum specifically so the HDMI implementor can provide some specific info for your specific setups.
I am sure it has been said he before, posting "Apple, please fix" in these forums is 100% useless. You have to report them in the Apple bugtracker system. But, with HDMI, you'll do much better asking on avsforum. Unless you can find that 100% of the time for all owners on a certain tv, a certain tv does not work.