What your employer is doing is perfectly fine as long and the amount is not excluded form box 1 of your W-2. In fact, TurboTax has specific provisions for allocating such contributions to the spouse who owns the HSA. Given this restriction, the HSA contribution should be shown on Schedule 1 as a deductible contribution.
"After searching these forums I figure out that the question is actually asking if coverage was held in persons name and not if they were just covered."
Whoever has said that is wrong; this falsehood seems to be perpetuated by numerous (but not all) TurboTax employees. Your original interpretation is correct. Your wife is covered by the family HDHP plan (and has no disqualifying coverage), so she is eligible to have HSA contributions made to her HSA on her behalf, including through your employer. There is no requirement that the HDHP policy be in her name.
