Service Fuel System

If the car displays that message and sends the fuel gage to E that means there could be a problem with the fuel transfer system or one of the fuel level sensors.
The C5 and C6 cars have two tanks behind the seats. Fuel level sensors monitor the fuel level in each tank and there is a "jet pump" that transfers fuel from the right tank to the left tank at all times.
The computer monitors the sensors to make sure this fuel transfer is occuring and if the sensors behave in a way to indicate that the fuel transfer is not working properly the computer will set a DTC (code) make the fuel gage to E and display a warning on the DIC. This uses a new style FFS fuel system (a corvette designation.
There are a couple of experiments you could run to determine the cause but if I had to guess I'd say you need to get the fuel sender replaced in the right side fuel tank. Sometimes the orifice doesn't work right and the fuel transfer won't happen. Meaning you'll never get the gas that's in the right tank.
There are other possibilities but that would require some diagnosis.

If need be I can give you some ideas to pass along to the dealership technician to help him diagnose this problem properly.
I am new here so I might be hard to contact.
I am a little wary about posting my email address but I'll try to be sure to activate the feature that allows members to email me.