NIMS is nothing more than incident command with a common format.
Does your department have SOG's against using incident command? I am presuming your department doesn't provide EMS services which are provided by a third service. I am also presuming that there was some head butting on a call between fire and medical.
If there is an issue with having a unified command at an EMS call, that would and should be addressed by the administrations of both services. It just takes cooperation between all agencies involved.
Okay this was the situation we have a guy that is going to school to be a emt but failed the test , We had a call and he always respondes in his personal vehicle so he can be the first one there , The call was a man with chest pains so he ordered the bird to be dispatched then the lz he was sending it to was not a lz anymore due to construction so the asst. chief radioed and told them they needed to devert some where else after the bird had been launched it was 5 min out and the one that had said launch the bird ordered it aborted ( he did both before medical got there ) should he have done this the guy ended up saying he was feeling okay.