And, most air bosses don't hesitate to use that authority. I've air boss'd around 40 shows, and in that time I've stopped shows because the on-field ambulance went off-field transporting a spectator with a heart attack, I've demanded that CFR wear full gear despite the 90 degree+ weather, I've delayed shows while the CFR equipment responded to small grass fires started with the pyro, etc. And I never, ever, allowed a show to start or proceed unless the CFR equipment is staged, beyond the crowd line, with direct access to the runway and operational environment-- which will generally provide a response time to the runway of 60 seconds or less.
The CFR crew must also provide a means to exit the airport property (cutting through fences, etc.) to enable the fastest response possible in the event that an accident occurs off-airport. And, in what I call the "Charlie Hilliard" rule, there must be a forklift or other piece of equipment available that is capable of lifting or righting an aircraft that winds up inverted on the ground (as was the case in Eddie's accident). In those 40 shows, BTW, I've never had a CFR crew object to anything I've suggested or required-- if anything they go above and beyond the agreed upon criteria.
All that said, when the air show takes place at a military base, different rules apply. The military has their own protocols, and they trump anything us civilians want. One of those protocols relates to staging: as I understand it, at the time of Eddie's accident, the military protocol in place was the same protocol the base used for normal air operations (ie, the equipment was on standby, in the fire house, not at the runway).
In the interim since this accident, the Air Force has agreed with ICAS to make a change to their SOP, and will in the future treat air show operations with the same protocols used when they have a known, declared, imminent emergency-- they will stage equipment near the runways, as is done at the civilian shows.
Note, the air show pilot has even less input in these decisions during a military show than he does in a civilian show: his only choice is to observe the protocols in place and make a go/no-go decision based on them. Similarly, at shows held on military bases, the air boss usually has little influence-- most military shows use their own air boss (at one I'm aware of, the only criteria to be assigned the role of "air boss" was to be unfortunate enough to be the most junior officer in the unit). Such military air bosses often have neither the training nor the clout to insist on hard-and-fast safety protocols, as their civilian counterparts do. Some military shows do bring in a civilian air boss, if not to actually air boss the show, then to assist-- but their position is usually considered only advisory in regard to matters such as CFR operations, which are already governed by the strict military protocols.
In Eddie's case, there's is ample evidence to suggest that, had civilian CFR protocols been in place, the accident might have been survivable. The fact that the Air Force has already agreed to amend their protocols during air shows to mirror their civilian counterparts may indicate that they realize this was the case as well-- and it will be interesting to see to what extent this decision may influence the outcome of the pending lawsuit.