My wife's employer had put me on her health plan after I provided paper work stating I was covered under my employers benefits plan and billed her for myself and our 3 children and won't refund her the cost to cover me all year. We reviewed the plans and they were considerably lower without me on it So I kept my companys insurance. Now after discovering that my wife contacted HR to have the difference refunded after confirming she provided all paper work that was needed at the time of enrollment. Her HR department is stating "the cost would've been the same" after reviewing their plans again it wouldn't have been the same and now they won't refund the money. Does my wife have a case?
Without a Country named, only a very generic answer is possible .
Generally, insurance cannot be retroactively reimbursed, because you could be taking advantage of protection without paying for it.
For example, imagine you pay for life insurance all year. if you die, the life insurance would have to pay millions. if you survive, you just claim that it was an error, and get your money back. obviously, the insurance cannot accept this, and needs to protect itself from it. therefore, nearly all contracts contain wording that allows you to get only money back for the future, not retroactively.
Your case his off course slightly different, as you claim you gave them the paperwork in the beginning of the year. they should have realized that you do not need insurance through her. however, they will claim that you should have realized that you are paying for it - and if you would have fallen seriously ill, you would have been able to draw payments from them. As long as they take your money, they have no position to deny such claims.
Note that most countries allow double health insurance, although it is most of the time pretty useless to do it. It is not their task to tell you that you are wasting money.
Without knowing country (and potentially state), it is impossible to give a clearer answer - legislations can be very different in different countries.
Although I think you have little chance of getting money back for past periods.