As others have said, it is not an issue with JUST the Integra AVR. It almost always a combination of things. Just because you bypass the AVR and it works, does not mean it is actually the AVR causing the issue.
You have to look at the entire signal chain!. Every time you add devices into the signal chain it changes how signal levels, bit errors, and voltage are EVERYWHERE in the system.

If Brent's diagnosis is correct (high probability it is), then just changing the AVR may or may not fix the issue (depending on how other brands deal with the hot plug). Changing the Sony TV could just as easy fix or not fix the issue as well, if it is a Hot Plug issue.
Changing the TV would be the most expensive, the AVR the next most expensive, the Ethereal HDM-VCT the least expensive and guaranteed to work (if it is a Hot Plug issue).