No reason why they shoudn't be allowed if as you say there is nothing else unusual or detrimental to their health. It would cause problems should said person be wounded/injured, and as syledis has said there would need to be a way of labeling, whether on dog tags or under blood group.
Interesting case, there must be prior examples of this.
yea the problem comes for chest drains etc where if you get it in the wrong side you can puncture the heart! In an emergency you might not see the dog tags especially on the ground or if the tags were blew off!