I don't disagree, and that is an easily imaginable scenario. But much like the cop they can still make things at best, uncomfortable, or at worst, nearly intolerable, for you. Creating that sort of de facto requirement is where the real problem lies (there's no legal obligation, but most of those vehicle search requests are performed anyway).
We already have employers requesting "voluntary" disclosure of health information (e.g., cholesterol check) as a condition of continuing group insurance coverage. Since it's illegal to require this information, they make it voluntary - but anyone who opts-out also opts-out of a hefty premium "discount". In reality, the "discounted" rate is closer to what employers would expect to pay for comparable group plans, while the non-discounted premium is high enough that 99% of employees line right up to have their blood drawn by the visiting nurse (conveniently stationed in the conference room down the hall).
Tangentially related, I've been wondering if that could affect current gender discrepancies in the entrepreneurial scene (prospect of paying 200-300% more for private health insurance than male counterparts makes it even harder to leave your day job). More female startup founders in 2014, maybe?