I know you are mocking, but the metabolization of alcohol within the body can be considered as an exigent circumstance that would allow blood to be drawn without a warrant. Generally speaking, States have an implied consent law in place that allows for law enforcement to draw blood from drivers suspected of being under the influence without a warrant in fatal or serious bodily injury wrecks. The Missouri v. McNeely case recently complicated this somewhat and requires law enforcement to get a warrant for blood draws. ..except under certain exigencies. Again, time and metabolization of alcohol / dissipation of evidence are exigencies to be considered.
The interesting thing about this case, is I haven't heard anything about probable cause for the blood draw - either under implied consent, or a warrant. I'm not exactly familiar with Utah laws on the subject, and am just speaking on general terms (dui laws are pretty standard across all states, since the Feds will withhold money from states that don't adopt their NHTSA suggestions). Its possible that Utah attempts to draw on all serious bodily injury or fatal wrecks. In Florida, we need consent, a warrant, or exigent circumstances.
BTW, the safety of the drunk in the hospital is not my concern. They are in a hospital for Cripes sake. My concern is making sure that I get accurate evidence that will lead to an accurate investigation, and if necessary lead to a prosecution to hold them responsible for maiming or killing an innocent person while driving impaired. God forbid you are ever on the wrong side of a drunk driver, I'm sure you would want law enforcement to do everything legally possible to get justice for your loved one.