My battery also became swollen, but I was not too concerned because it was working just fine. In fact, I did not realize that it was swollen; I thought that the case had just popped apart. I happened to be in the nearby big city with an Apple authorized repair facility, so I took my computer in. The clerk took one look at it and said, "Oh, you have a pregnant battery." He checked my warranty and said that my Apple Care was in effect. He took my battery back to the technician, again referring to it as a "pregnant" battery, so indicating that this was a problem that they had seen before. The technician said that he could not do anything with the battery to determine if it was defective. I would have to leave my computer there for a few days so that he could hook it up to diagnostic equipment, get it to throw codes, send the codes to Apple, and see if it was covered under warranty.
Well, nope, there was no way that I was going to be separated from a working computer which I use all day long, every day, so that they could have it sit on a shelf until they got around to verifying that the battery was working, but swollen, and needed to be replaced under warranty as defective. I did not leave my computer there, but took it home. I did follow their advice and take the battery out, so that I am running the computer without the battery.
I then went on-line and at Apple Support filled out all of the information to receive service directly from Apple. This morning, I talked to Apple; one person verified all of my information and then transferred me to a special department for battery issues. The second person, verified the condition of my battery (at first saying something to indicate that he had never heard of a swollen battery, but later mumbling something that indicated to me that this was not an uncommon complaint). He said that a new battery would be shipped to me and I should return the old, defective battery in the same box. He did take a credit card account number to hold the funds for the cost of the battery until they received the old battery back. There was no discussion about whether this was covered or not, nor the need to inspect my battery, just the need for me to actually return the defective one.
It might have been different if I could have gone to an Apple Store as opposed to an Authorized Repair Shop, but the closest Apple Store is over 2000 miles away. Dealing directly with Apple over the internet and phone seemed to work fine for me. Once this is all resolved, I am going to go to the store that was not very helpful and tell them what happened with my "pregnant" battery that they would not replace.