OK, here's what I tried.
PS3 on, Onkyo on, TV off, all cables connected, insert CD into PS3 -> CD plays as expected (I have auto play on for the PS3)
PS3 on, Onkyo on, TV off, disconnected optical out from TV, insert CD into PS3 -> CD plays as expected
PS3 on, Onkyo on, TV off, disconnected optical out from TV and HDMI out from Onkyo, insert CD into PS3 -> CD plays as expected
PS3 on, Onkyo on, TV off, disconnected optical out from TV and HDMI out from Onkyo, insert DVD into PS3 -> DVD plays as expected
Basically, all scenarios worked as I think they should.
Now, as for what Caleb just said is somewhat true for me. As shown above I can play a CD while the TV is off just fine. If I turn on the TV while the CD is playing then it cuts out for a second but then resumes playing. It doesn't go to the menu but I'm assuming that's because it's a PS3. Not sure. If I turn off the TV while it's playing then it cuts out for a few seconds but then resumes just fine.
I really don't think it's an HDCP issue. Jason, I would try disconnecting all your a/v equipment except the DVD or PS3 and remove the HDMI to the TV and see what happens. That will isolate the exact scenario you want and hopefully that will work and then you can one by one add back in the other connections and see when it stops working.
Bryan