Paid upfront for health care, help deciphering bill

Long story short – friend needed to go into Detox immediately, I paid for it on my credit card and was told by the Detox facility that they would charge me ($6kish), they would file a claim, and then whatever the insurance covered of the bill they would refund.

Months later finally got the claim information – can someone help me decipher and see if I need to be going back to them facility about a reimbursement (which may be a lost cause but would still like to try)?:

Claim total (Amount billed) for 5 nights was $20,500.

Discounts and reductions applied: $16,900*

*(The billed amount is greater than the allowed amount for this service.)

Amount Covered (Allowed) is $3,600.

Health Plan Responsibility is $2,880.

Your total costs: $720

It then states that total covered benefits approved for this claim was $2,880.

So can someone help me decipher? Detox center tried to bill $20500, insurance said you can bill $3600 and we’ll pay $2880 while patient owes the $720?

Is that all separate from the $6k I paid, or should I be calling in saying I should be getting refunded my $6k minus the $720?