Cauterisation is not a myth. Medics from all eras have used to seal wounds. From having a hot poker stuck in a arrow wound to Victorian hospitals who used more advanced but pretty basic and medieval practice compared to todays evolved scientific methods. A very hot metal can and will cauterise a wound, but in this scenario there was probably a variable in the arteries being pinched and closed by the speed of the shrapnel, crushing of the limb or simply the gentleman was incredibly lucky to have not bleed out or die of shock.

The reason Army medics wouldn't use cauterisation in the field would be because it is dangerous, uses tools that you can't easily control in the battlefield and using tourniquets + pain medication stabilise the patient more affectively for recovery and rehab. If a leg is blown off with sufficient heat it can cauterise blood vessels but you wouldn't want to practice this because of the risk of infection and shock. Burns for example, which obviously create huge risk for infection and loss of fluids and death if not treated quickly and in the right facility.

"Cautery was historically believed to prevent infection, but current research shows that cautery actually increases the risk for infection by causing more tissue damage and providing a more hospitable environment for bacterial growth." SOURCE: The american journal of surgery.

Obviously we still use cauterisation in certain circumstances in Hospital today. Actual cautery which is the type mentioned in this post are few and far between in 1st world medicine. We mostly use electrocautery and chemical cautery, but in a Burn unit you wouldn't use it due to the major risk of infection and complications of shock.

Without being insensitive because it is awesome you are a RN this person maybe telling a family story as they know it, rather than how we in the medical field would understand it. I don't believe everything I read on the internet, but I also wouldn't go into a church and tell a group of people that God is a myth. This guy isn't hurting anyone but telling his family story.