You added the parts about “facing imminent death” and “if you have no other option,” which make an important difference. Those don’t need daily promotion from the president of the United States. If anyone is on the verge of death and a doctor says “I recommend trying this experimental treatment, would that be okay?,” virtually no one would reject it, whether they heard the president say anything about it or not.

Public promotion from the president and some of his most prominent allies — such as popular media figures and his personal attorney — has an effect that’s much broader than someone facing imminent death being open to a treatment with some potential, but still uncertain side effects and effectiveness.