Fully agreed, paying all, or most, of the insurance tab doesn't mean you get a say in medical diagnosis or treatment of those covered.
This isn't so, so long as there are variations in what you can pay for. For example, I can decide to pay all the costs for vision care, or not. The treatments covered under a policy are directly related to the provisions of the insurance contracted for and the price paid. Some policies will cover chiropractic care, some won't. Maybe I'd like to have homeopathic treatments, but my employer is unwilling to pay for a policy that covers them.
There is no particular shield in place, except when certain coverage is mandated and except that I must treat all employees with the same coverage the same. So, for example, I can't simply step in as an employer and say employee X won't get vision care if I pay for it for their peers.
This is just as true for healthcare paid for by the government. If Medicaid doesn't cover some treatment, it is a consequence of the the prior arrangement between the government and the healthcare system they've contracted with. The one footing the bills absolutely has input in these matters, even when the bill payer is the taxpayer.