Hmm, it's weird that it doesn't work quite as good for chill's device. I actually only have both of the HDMI ports occupied at the moment, and I'm still able to switch to all inputs -- including Component which is currently bugged out in Pierogi -- using the regular remote. Chill, I presume you have tried all three keysets (1/1a/1b)?

The problem switching to HDMI might, as you say, be due to no active signal (or at least no connected cable) but I'm not sure that is the case. If the behaviour remains when using the regular remote, it's obviously intended to be that way, so that might be something to test.