Most common example is probably motor vehicle accidents where firefighters (in concert with police officers) will secure the scene, gain access to the vehicle(s) if necessary, etc.

A lot of firefighters are also EMTs and paramedics. Both because in places with volunteer firefighters they can just work as EMS, and also because there's quite a bit of overlap in that if you need a firefighter there's a decent chance having EMS around would be beneficial as well.

Firefighters who aren't trained in EMS are not providing medical care, so saying "leave it to the professionals" is pretty dismissive in this context.