A. The topic of medical insurance is occupying a lot of people right now. Insurance in general is a wonderful financial product that enables us to buy protection against risk and loss. By paying a small premium to the insurance company, we are protected against a large loss should we incur an insurable event such as illness in the case of health insurance, accident in the case of liability insurance and so on.
Insurance is an ancient institution and in fact mutual insurance is mentioned already in the Tosefta, a collection of law dating nearly to the time of the mishna almost 2,000 years ago:
Donkey drivers are empowered to say: anyone whose donkey dies, we will [collectively] provide him with another donkey. If it died through negligence, they don't have to provide him. If it is not through negligence they must provide him, and if he says, "Give me [money] ; rather, they buy one and give it to him. (1)
This Tosefta describes two properties that characterize insurance to this very day. The first is that insurers strive to keep insurance from being an excuse for negligence by limiting coverage if the insured contributes to the loss through carelessness. ("If it died through negligence they don't have to provide him".)
The second is that the basis of insurance is indemnification or reparation. The idea is not to provide a monetary payment to the insured, as would be the case with a financial derivative. The object is to restore as closely as possible the situation that existed prior to the loss. That is one reason why the driver cannot demand money instead of a donkey. (The other reason is that the other drivers want the insured to participate in the care of the donkeys; the work is shared among more members of the caravan. But this reason too is ultimately connected to the idea of restoring the original situation.)
This idea is relevant to your question. The object of your health insurance is not to provide you with a particular cash payment whenever you encounter a given health problem. The object is to make sure your medical bills do not swamp your budget, even if your treatment is quite expensive. If you are entitled to some kind of rebate on your bill, then your loss is less and a smaller sum is needed to indemnify it.
The noted rabbinical authority of the last generation, Rabbi Yitzchak Weiss, related to a similar situation in a responsum. A person lent his car to a friend and the friend had an accident. The insurance company paid for the loss, but the owner wanted to collect from the borrower also, since in Jewish law a borrower is generally liable for any kind of loss.
It would not occur to any moral person to request recompense from the borrower insofar as he is already getting a settlement from the insurance company, and it is against the law as well. (2)
There may be many relevant details in your case, such as whether your benefit is truly in the nature of a discount (meaning that in the first place your insurable bill is smaller than originally printed) or whether it is a repayment, in other words, a type of insurance in itself (meaning that you have double insurance, a common situation). So it is impossible to provide an authoritative answer to your particular question without more information. But the basic ethical principle is clear: Insurance is meant to protect the policy holder from a loss, not to provide him with a gain. So if the insured is entitled to discounts or extra benefits from other parties besides the insurer, he needs to carefully examine the insurance agreement to make sure he is entitled everything he claims.
SOURCES: (1) Tosefta Bava Kama 11:25, see Babylonian Talmud Bava Kama 116b. (2) Responsa Minchat Yitzcha III:126