It is recordable. But fails your other needs.
1. It's 1080i
2. It's not a HDTV Camera. i.e. what you would use for HDTV broadcast use.
My bet is this is partly limitations of the chips and partly limitations of HDMI. HDMI mandates HDCP and the FINE PRINT about this means that streams are paid one by one. There's more to this than I can write here but the cost issue alone means there is no way to meet target prices and put out 1080 while recording.
There are other issues with HDCP that I didn't discuss here but that explains the drop to 480 easily. If you have a HD display, and it displays HD then any passthrough shall be SD. And that's exactly what happened when we hit record.
-> After this and many other nuggets I don't think HDMI is that friendly to those that want to use it for creative purposes.