I don't know how things were run in the '70s, squad responding alone on calls vs engine and squad.
In today's world LACoFD (as well as most, if not all fire departments) sends an engine and squad on every medical response, day or night. LACoFD also sends a private ambulance at the same time. If the call is in a bad neighborhood then the police or sheriff responds as well.
In the case of LACoFD a squad covers their own district as well as two or three engine companies in neighboring districts.
If the engine arrives before the squad the crew evaluates the patient and if the paramedics are not needed the engine cancels the squad and the patient is transported by the private EMT ambulance sent to the scene.