In San Bernardino we don't have this issue. We have a "first available" co-existence policy. However, our sheriff's department handles SAR operations on the ground. The SAR members are in the SBCO chain-of-command. I have worked with a foot in both worlds. In the last 12 months I have worked on three operations that were directly related to the saving of numerous lives. Two were mountain rescues and the on-scene control was SBSO. However, due to physical limitations all I can do was work the radio's now. I worked the initial with SBSO who transferred ground operations to SBCoF. I communicated directly with the IC over CALCORD for 11 hours guiding fire resources to 3 people stuck in the snow during a blizzard. All were hypothermic. Once on scene my job was done. I went to sleep while SBCoF spent 3 hours extricating the victims who arrived at ER three hours later. They knew to expect them because I also coordinated medical from a limited perspective. On another ground incident I was first medic on scene of a head on collision and instead of coming up on SO I came up directly on fire. That what was needed at the time. My patient died nonetheless. "Blood Alley" Hwy 395. Yes, I have a radio identifier.
The point is not how awesome I am. I spent time as a LEO until injured. During this period I worked SAR radio. After rehabbing for 20 years I worked SAR ground and then became a PCF. I was therefore trained by both sides and knew where each was coming from. I believe this is what is missing. A candid conversation between the PILOTS/CREWS about how they may coordinate between themselves. "40 King 1, Air 6 - What can I do to help you? Air 6, 40 King 1. Can you watch my rear rotor? I'm up close to the mountain... 40 King 1, Air 6, roger. You're clear by 6 feet." Get the brass out of it!!!
As I've said we don't have a power play between both agencies. If anything one bird will hover out of the direct zone while the other extricates. Depending on the situation SO will land at a LZ and transfer the patient to SBCoF unless air transport is critically necessary for life saving without a transfer. Our deputies are trained paramedics and can handle the medical needs. There is no need for a pissing contest.
I think that this well publicized series of events was embarrassing to both agencies. I've seen it before. But think about this. I know from experience that my POC was the deputy in charge on the ground who was in charge of SAR - sort of. They are given latitude to do what is necessary. ICS protocols transferred operational control to Fire. During one operation I was involved when all three entities communicated together for one purpose - to save the lives of those in danger. It was all about coordination for patient benefit and that should be the goal.