I'm only really familiar with Los Angeles County Fire Department from the late 80's to 2000's. All LA Co. firefighters are at least EMTs, while most are paramedics. Ambulance personnel are usually only EMTs, which is a lot less training that paramedics.
Firefighters do not get paid during their time off as the OP claimed. They usually work 10 24-hour shifts for about 240 hours per month. That is more than 55 hours per week and it's not all eating and playing cards by a long shot. During their "down time" they have to cook all their meals at the firehouse, maintenance their equipment, clean and maintain the firehouse, patrol problem areas, and continually train. Anyone who thinks it's an easy job is a fool.
Calls come in at all hours of the day and night, and it's very rare for a crew to get 8 hours sleep while on duty. They provide emergency medical aid, cut cars apart to pull injured people out and perform all kinds of rescues under all kinds of situation. In Southern California brush fires were a big thing. I've seen exhausted crews come off the line at a brush fire for a short rest break sleeping in the middle of the road with their heads against a curb.
I've also heard fire dispatch come over the radio to ring the "last alarm" bells for fallen firefighters "returning to quarters" for the final time after giving their lives in the line of duty. I've seen a burly firefighter crying after performing CPR on a toddler he pulled from a swimming pool but couldn't save. "Fill them all in with concrete," he said to me.
Some firefighters can be real assholes, especially the old school guys back in the 80's and 90's when they didn't stress being PC as much. Still, I never met one who wouldn't risk their life to put out a fire or keep a dying person alive. Hero? I don't know, but if you meet a firefighter who hasn't saved a life they are probably new on the job.