I think it's really up to the district (or state) in most cases. Federally, there's no requirement for the nurse at all. It requires the parent, one regular ED teacher, one special ED teacher, and a rep of the district. The school or parent can ask for other qualified people (which is what brings in the nurse).
In our school, our RN addresses students who need medical intervention as part of the IEP/504. My role as the discipline office nurse is to interpret how school discipline should consider this child different than the norm.