The battery certainly is covered by the Voltec warranty, up to 8 years/100,000 miles. I wouldn't have bought my Volt if they didn't offer this warranty.
You SHOULD be able to get someone at Chevrolet to acknowledge that! Keep trying and go up the ladder as necessary. If you have the warranty manual that says it is covered, and they are saying it isn't, I would make an appointment to see the district manager and show him the warranty booklet in person. And if he still denies coverage, say you want it in writing, with his signature. Then send a copy of that letter along with a copy of the warranty booklet saying it is covered, to the GM CEO (Mary Barra). Be very polite, apologizing for having to bother her with this, etc.
Do not waste time with anyone between the district manager and Mary Barra. Go right to the top!
I used this tactic once when I had an NEC laptop (6 of them, actually) with various problems. I kept returning them for another one and finally was talking with the guy in charge of NEC in the USA. In fact his secretary knew who I was as soon as she picked up the phone because she recognized my voice from calling so many times. The USA head guy finally said he couldn't do anything for me and said just go exchange it for another. I reminded him I had done this SIX times and each laptop had a different problem.
So I decided to look up who is the top boss of NEC. He was in Tokyo. I had his name but not an address. I sent a letter to the company headquarters in Tokyo with ATTN: his name. In the letter I detailed the problems with each laptop including serial numbers, etc. I apologized for bothering him but said I had gotten no help from the USA boss. I said I really liked their products and just wanted to get one that worked. I figured I would never hear back from him and would have to just get my money back and buy from one of their competitors.
I never did hear directly from the NEC head guy in Tokyo, but about a month later I receive a call from Mr. USA boss and he is grovelling, asking WHAT can he do to keep me as a customer? Since the factory the laptops were made in was in the same state as I lived in, he offered to pull 2 laptops from the production line and extensively test them for 2 weeks. Then I could meet him at the factory for a tour and select whichever one I wanted. I said that would be acceptable as long as at least one of them worked!
In the end he was too busy to fly out for the factory tour, and I had already exchanged for #6 at the store. Wouln't you know it, it also had a problem with a little screen brightness slider? I called Mr USA boss back (who was now VERY helpful) and he had 2 engineers from the factory meet me at my office. They were sure they knew what the problem was. They disassembled the laptop and discovered it was a different problem and required a soldering iron to fix. They had not brought a soldering iron, but since it was lunchtime, I was able to take them to one of the technician's benches (who was out to lunch) and they fixed it there. Then they said they were instructed to take me to lunch, anywhere I wanted, and NEC would pay. Now we're getting somewhere! See what I said about going right to the top? Since all 3 of us were engineers, we had a most interesting conversation over lunch at a nice steakhouse. They said I was famous in their factory. The big boss in Tokyo had sent a copy of my letter to EVERY employee in that factory! They explained that their factory had been tasked with taking over worldwide production and the laptops were being produced so fast that many with problems were escaping before being detected. One of the engineers said if I had any more problems, just drop it off at his house and he would take it to work with him and get it fixed.
Well, that's a long story but I like to tell it once in a while. Just shows what kind of results are possible if you go right to the top. A friend of mine once had a problem with an HP calculator, he wrote a letter to Mr Packard and got similar results.
Good luck with your battery, I'm sure it will eventually be fixed under warranty.