Wearing of bracelets, rings or precious gems with the belief that these are a form of protection is shirk. What if someone wears it believing that Allah alone can cure a person but these accessories are simply means of achieving the purpose; Allah will put shifa in these means?

A person went to the doctor and got a prescription. Instead of taking the prescription to a drug store and buying the medicines, he simply rolled the prescription and tied it around his arms or neck believing that in this way he will be cured. Does this make sense? Undoubtedly, the answer is no. The situation you described is similar to this.

If a person "sincerely" believes that Allah has the power to cure, then on what grounds is he trying to justify his act of wearing amulets or bracelet, etc?

Is there a single hadeeth where Muhammad (ﷺ) or his Sahabah (رضى الله عنهم) wore bracelets/amulets etc in such a way? Rather, you will only find a hadeeth in Musnad Ahmad where Muhammad (ﷺ) said that the one who wears an amulet has committed shirk.

Are we trying to deny the teachings of our Prophet (ﷺ) and saying that we know better?