The secondary insurance carrier is telling you that the amount that was paid by the primary insurer eceeds the amount that they would have paid on the same claim. Health care providers typical have a negotiated rate and which they provide services to insured members of any given health plan. Once you are paid this negotiated rate by the primary insurer, the secondary insurer has no obligations to pay more. Treating a patient that has two health insurance plans is rarely beneficial for the health care provider, unless the negotiated rates that you are contracted under are higher with the secondary insurer. If it was, then you would be able to collect the difference in that amount from the secondary insurer. In the case that you eplain, the patient should be the one responsible for paying the balance that was unpaid by the primary insurance company.

I have an example where a dentist in California has a contracted rate with Delta, which paid 90% to the contracted rate. The secondary insurance, Guardian, did not have a contracted rate with the dentist. Still the secondary insurer only paid the remaining 10% of the primary's contracted rate, and called the patient's responsibility $0.00.
The dentist disagrees, and claims the balance to the non-contracted rate is owed by the patient or secondary insurer.