For situations similar to what is described here, almost certainly not.
You are free to deny treatment or services. You can give medical power of attorney to someone you trust to approve or deny treatments if you are too ill to make decisions on your own. You can complete an advanced medical directive to tell whoever is making decisions on your behalf what sorts of treatments you want and what sorts of treatments you wish to avoid.
If your goals are financial rather than medical, however, these are unlikely to be helpful to you in the sorts of cases outlined in the article. In the case described, it is unlikely that a reasonable person could have determined the cost of the air ambulance in advance. The doctors that are trying to get the patient moved have no idea what the air ambulance is going to cost or what insurance is going to cover. The insurance company would know what is covered. The air ambulance company would likely know what it was going to bill (though it is terribly unlikely that the company would make that information easy to obtain). But it is highly unlikely that you could figure out from the hospital which air ambulance company was available, call the patient's insurance company, and determine what the the company would cover, then call the air ambulance company and find out what they would bill before a decision had to be made. When the doctors say that we have to transport the patient now, you don't have hours to spend on the phone trying to get someone to give you billing information. Similar issues potentially arise when the patient gets seen by a different provider, not just when they get transported from place to place, so you'd have to be on the phone constantly with insurance to understand what the bill was going to be.
From a human standpoint, you'd also be asking your loved ones to value your money over your life which is very unlikely to happen. Maybe you could find a cold-hearted stranger that would be willing to be your medical power of attorney (for a fee, I assume) that would commit to denying any treatment that would impact the amount your children would inherit upon your death. But if someone I loved was in the hospital, I'd gratefully authorize an air ambulance to save their life even if I knew that it would be terribly expensive and that they had expressed a desire not to have expensive treatments. I'd much rather have the person than the inheritance and I'd deal with them potentially being upset after they recovered.