1. What kind of race track are we talking about here? A horse or dog racing track, where those requiring medical attention are probably spectators or staff? Or a race track for cars/ATVs/dirt bikes/etc. ... where EMS could be responding to a crash? I'm thinking it is the second scenario since you specifically reference immobilized patients, indicating some traumatic mechanism of injury.
2. The protocols for requesting medical command and for the circumstances under which a patient can refuse transport vary widely from state to state.
3. IF (and I stress -- IF) it is the case that staff of that EMS service are clearing c-spines of patient inappropriately ... well, all I can say is ... the FIRST time that someone is cleared by EMS and later presents to an ED with a significant injury ... that service will be out of business, pronto.