My wife recently accepted a job at which she will receive a 175% match for all HSA contributions, but she must be enrolled in her new employer's HDHP plan to obtain this benefit.
For this reason, we would like to enroll her in her new employer's HDHP plan to receive the HSA match, but also keep her on my medical plan as the family deductible is much lower. The math works out such that even with her premium in consideration we will still be net-positive with her 175% HSA match.
We never intend to submit under her plan for any sort of medical claim, but rather always use mine. We will only use her plan for the HSA match and nothing more. We will use both hers and my HSA accounts to pay the deductible down on my HDHP plan since it will be the only plan we will claim against for medical expenses.
Being that no medical claims will ever be made against her policy will mine be considered her primary insurance? I do not know if once a claim is submitted for her under my insurance if there is a way for my insurance to find out that she is actually also covered by her own employer.
Sorry, no. She can't make contributions to an HSA unless she is (1) enrolled in an HSA-eligible HDHP plan, and (2) has no other health insurance coverage. (It doesn't matter that you say you plan to not make any claims -- the coverage exists, therefore she would be ineligible to contribute to an HSA.)
It's not the insurance company you have to worry about, it's the IRS. (Although she probably will have to sign a statement certifying to her employer that she has no other insurance coverage in order to get the match.) You have to certify on your (joint) tax return that she is covered by an HSA-eligible plan and has no other insurance coverage. If you get caught, you owe back taxes, interest, a 20% penalty for ineligible contributions, and possibly an additional 25% penalty for knowingly filing an inaccurate tax return.
You will need to decide to continue her coverage under your employer's plan or drop her and have her covered by her employer only. Of course, she can be covered by as many policies as you want -- she can be covered by both plans, she just can't make HSA contributions.