phuz, I think you have covered the bases with your AVR. I quickly read through the manual for your unit and the SR800 operation is fairly common with Onkyo products.
1. Direct Mode: The manual says "minimal" audio processing which I take to mean that the only digital action is the required D to A conversion of digital inputs (HDMI, optical, etc.). If the SR800 is like my 805, then there is no bass management or any other digital processing available at all in the Direct Mode. This lack of digital processing is the reason you do not hear the delay in audio as you describe.
2. Unlike the Denon model(s) described by AcuDefTechGuy, there does not appear to be a Direct + subwoofer mode in your AVR. If there is, I could not find it. Although the manual does say right below the "Direct" description that when in the "Stereo" mode the subwoofer is active so some digital processing is in play in this mode, but apparently not enough to cause a detectible audio delay.
Sorry, but I think you have discovered the one limitation in your and your friend's AVR that while a big problem for you guys with how you use them would not be an issue for most users.