Synchrony Bank Credit Card Complaint

Synchrony Bank Credit card department,

Credit card protection / Debt protection Tennessee

My wife and I were at a hotel in South Dakota, and the next morning the phone rang and the caller said they were the front desk and there had been a computer malfunction, and they needed her card number again. SHE gave them the card number, as I walked into room. She told me what I happened and I immediately went to hotel front desk, figuring she had been scammed. We called the credit card company immediately, to report the fraud. and there was $2800.00 billed to our card already.We received a letter, from Syncrony fraud division, we filled it out and sent it in. We thought that was the end of the issue. Today I received a letter From Synchrony stating the fraud was our fault and now we owe them the $2800.00. My understanding is they are not following the law themselves, by trying to get consumer to pay for the fraud