How tough was President Hayes? Via a link I received in the comments, I found a site called the Washington Pugilist. It has an article titled On Hayes.
The site notes:
A civilized lawyer who lived a healthy, comfortable life before the war, Hayes grew stronger and fitter as a soldier. "Ruddy" was one of four Civil War veterans to become president, and while all were generals, Hayes was the only one to be injured; fantastically, and repeatedly, as it were. Five times he was injured, and had four horses killed from underneath him, one of which threw him violently to the ground causing a severe concussion--his second most serious injury of the war. He was believed dead more than once, so convincingly so that his death was reported in the press. One thread which weaves through each tale of narrow escape is that his ability to keep moving despite devastating injuries helped him avoid capture and kept him alive. This evasiveness and cunning would serve him well in a fight.
The most serious injury occurred at the Battle of South Mountain in 1862, when a musketball struck below his left elbow, splintering a bone and tearing a blood vessel. During the time of the Civil War, a man was unlikely to survive such a devastating injury. Not only did Hayes survive, but he kept his arm. His healing was described by medical historian Rudolph Marx as taking an "unusually short time even by modern standards," who likewise hypothesized that he "must have possessed rare powers of recuperation and an extraordinary resistance to the common type of wound infections." This, of course, does not prove that Hayes had superhero-like healing abilities, rendering him completely immune to all human illness and able to stop bullets with his head. But it certainly raises the burden of proof for those who suggest he didn't.
Of course, his ability to survive the bitter and highly disputed election of 1876 also proves his durability and toughness. This Washington Pugilist site looks like it is worth watching.