Typically, when you receive a form 1099-C for cancellation of a debt, it means that you did not actually pay for the amount you owed. The amount cancelled on a form 1099-C is included as ordinary income for the year you receive the form 1099-C.
There are a couple of exceptions. One of those is if it is an expense that would normally be deductible to you. In your case, medical expenses are deductible. This can get tricky though...and, we would need more details to be accurate. If the debt is an actual loan and it is cancelled, then it is true "cancelled debt". If the dental office sent you the 1099-C for normal uncollected medical bills, then that form was sent incorrectly.
It sounds like quite a bit was going on. The bottom line, if I am understanding correctly, is that it is cancelled credit card debt. It is not money you receive, but the credit card company essentially "loaned" you money. And, then they cancelled it (or at least part of it) ...through was sounds like a balance reduction. Am I understanding that correctly? If so, it is income to you.
What do you mean when you say "the amount they want is money that I'VE paid out to start with. " ? Thanks.