Join the club. Car was barely 2 weeks old and was nearly plowed into by a Wrangler because 'I' stopped, and completely, for no good reason. That was the first of several SBS incidents.
You can disable it as I do now every, single, bloody, time, I start the car. No more incidents, none, zero. I've experienced the 'BRAKE!' pop-up once recently w/ the SBS off and the RACC was engaged. Even though RACC is "supposed" to be gauging and maintaining the distance (which it does very well under ideal conditions) it is in fact incapable of handling the exception of objects suddenly and abruptly cutting in to its 'gauging space' in very tight quarters (lotsa traffic) at freeway speeds. It merely reacts after the fact, and poorly at that. Don't know if it would have literally braked or attempted to stop the car in any way (that would have ended badly if it had), most certainly would have based upon previous experiences if the SBS was enabled. I truly don't know what it would have done because I'd already anticipated the guy cutting me off prior to the car realizing it was happening and cancelled the RACC via cancel button on steering wheel, disengaging throttle giving the joker room w/o me having to apply brake and pissing-off the other joker tail-gating me. The current crop of automation has zero situational awareness.
Another exception RACC doesn't handle well... tight curves on the highway whereby the vehicle it's gauging, slowly via curvature, moves out of its direct vision path...it then accelerates if it had been following at a speed lower than its setpoint. The piss-poor behavior these systems demonstrate are clearly due to the vehicle's lack of peripheral 'vision'. In a nut-shell, half-assed automation that should not be in a vehicle at this time.
Anywho...Mazda won't (claim they can't, which I call BS on) make the SBS setting a permanent toggle OFF, because...it's a 'safety' feature. A liability issue to do so, so they say...I plainly stated I disagree and counter it's a rear-ender magnet. A different liability which I'm not partial to. I then asked the service manager to contact Mazda again regarding my request and get it in writing that they accept full responsibility, and liability, for the accident when I get rear-ended. When, not if. He/they both declined, verbally of course.
Maybe it's possible to permanently kill the SBS in your 3...can't hurt to demand they turn it off and see what kind of BS response they feed you.