A few MAJOR points for EMS response.
Always wear gloves. Mr Pincus touched the wound area not wearing gloves. Possibly exposing himself to blood borne contamination and possibly putting contamination on the wound from his hands.
Tourniquet - Mr Pincus mentioned using it for bleed through of the bandages. This is wrong. You place more bandage over the wound and continue to apply direct pressure with bleed through. He did get it semi-right when he talked about artery spray.
The only time to use a tourniquet is when direct pressure fails and the tourniquet is a last resort. One guy mentioned the old days and tourniquet misuse. That must have been a real long time ago because I have been trained in first-aid since 1975.
Buzzcock made the best general response for rendering immediate aid.
The high points - informing EMS that this is accidental. His comments about LEO's response were right on.
I like the quick response bag ideal, but such a thing needs to be in a sealed bag due to weather. It could also have a pen or marker and sheets of paper in it.As well as a couple pf pairs of surgical or Nirile gloves.
Most importantly. If you have not had at least an 8 hour class on first aid get one. And take a refresher every few years or expand your skills as you go.