I noticed the chirp after filling up with some cheap 93 octane. I filled up with Shell V-Power at half full and then ran two more tanks of Shell through and still had the chirps. I switched to Sunoco 93 octane at half full and have ran through another full tank of Sunoco and still had chirps.
I am now on to Valero 93 octane and filled up with about 1/4 of a tank of Sunoco left. I went out for a spirited drive last night and the crickets are still present. I'll try one or two more tanks of Valero again. If that doesn't resolve it then I'd have to say that the myth is busted. Not unless it has anything to do with octane rating, which would be a huge stretch. Does it look like there is a pattern with people from California reporting that changing brands resolves the issue? Maybe I could give another round stations a shot but this time with 91 octane.
The Valero by me has TurboBlue on tap

It is not of the unleaded kind though.