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No, you do not have to park it in Reverse (but GM recommends it). That particular battery drain issue was for the 2005 model year only. Your battery drained/died for some other reason.
There is a TSP however that was issued for revising the software for the electronic doors which addresses battery drain for the '06 and newer cars. Do a search using TSP as the keyword.
That is the exact problem with dealerships - very few Vette trained technicians. I was told the same thing about my 08. Not a fault of the people at the dealership - they have to be able to work on many different models. There just isn't time to stay up on every change in every model. How many Vettes come in for service vs other models? CF is the best place to find a good technician in your area.
There is a TSP however that was issued for revising the software for the electronic doors which addresses battery drain for the '06 and newer cars. Do a search using TSP as the keyword.
There is a technical service bulletin on the '05s that keeps the battery from drawing down all the way if you accidentally get NEAR reverse, but not actually INTO reverse. I had dead battery syndrome five or six times, and I haven't had it since the reflash.
Oh, and your dealer is misinformed. Dealers still tell C5 and C6 owners they have to have the doors closed when the car goes up on a lift or the frame will bend...and that's a C4 old wive's tale.